Why did Dr. Linda stop doing Lucifer?

Short answer: Because she's a professional and she knows it's wrong.

Long answer with intro: Whether Lucifer could control her is irrelevant, he can sway pretty much everybody who's not Chloe, but he's on Earth, more or less for the human experience. Influencing others is something he can turn up the dial on when he wants to and his sex appeal is pretty much always on. But doesn't need Dr. Linda for sex. That's not why he sees her. He wants her for her therapy and the sex is payment, not cause he needs her under his influence, cause he actually wants her mind working. He has sex with her, cause if he didn't, she'd be too distracted to give him therapy and he's there for the therapy. He's happy to have sex with her but he certainly doesn't need it.

Lucifer is fine with letting Dr. Linda and pretty much everyone have free will, this is made clear in the first scene (dialogue below), after Lucifer sleeps with the lady judge and he gets the judge to sign off on Dr. Linda working the case. Lucifer's manipulative like crazy but he's not controlling. He seems to enjoy watching and interacting with human behavior.

Script

Lucifer reaches for the files, Dr. Linda pulls them away

Luci: Oh, come on! I won't tell if you won't.

Linda: I swore an oath... to a judge.

Luci: Oh, did you now?

Linda: You only get to read the files I deem necessary for investigation.

Luci: (scoffs, sighs) Now, remember our deal. You have to fix the detective's broken douche meter whilst we investigate this crime. Mm-hmm.

Linda: I never agreed to that.

Luci: Oh, come now. Don't you want to help me? Hmm? Linda?

So, she's not lucifer's puppet, she's a professional. Perhaps he could turn up the volume and persuade her to give him the files, but that's so not his style. He'll take no for an answer. He might ask again 10 seconds later cause he's like a child, but he almost never forces what he wants on anyone except when he's angry.

The show, while corny at times, is good with details.

After Chloe shows up and after that initial meeting with Dr. Linda, she directs them to the first suspect (the jumper). Lucifer says "top work Sherlock" and playfully slaps Dr. Linda on the back and she looks distinctly uneasy. Now, at this point in the show, we're not sure why. Maybe it's cause he's walking away and she expected sex or maybe it's cause she's discussing a case with the police AND a "man" she's sleeping with, a case she should never have been assigned to and she's feeling a lack of ethics. My guess is the later, but there's no way to be sure.

. . .

A short time later when Lucifer invites Linda to Lux and they're discussing the second suspect, Chloe gets a call from Dan regarding Palmetto, her other case and she has to leave.

Luci: What, so that's it? You just go running as soon as Dan calls? What about the case?

Chloe: This could relate to another case I'm working on. There's units looking for Sandy now. And once they find her, they'll call me.

Bye. Bye. (Chloe walks off)

Luci (to Linda): Unbelievable. You see what I'm dealing with now, don't you?

Linda: I think I do, actually. It's worse than I realized.

Luci: Thank you.

Linda looks shocked that Lucifer doesn't realize "it's worse than I realized" was directed at him, not Chloe.

So, Linda, we can assume, didn't take Lucifer all that seriously at first. The devil talk, she assumed it was a metaphor, and he didn't seem dangerous, and he was charming and they were sleeping together, so . . . not something she does with any other client, but it was fun and seemed to her, we can assume, harmless.

Now she sees him as pretty much crazy. She doesn't see him as the devil, but she sees him as just bananas out of touch, where Lucifer thinks Chloe needs fixing. Dr. Linda realizes in that scene that Lucifer really needs a psychiatrist. She might never have had that thought before. The truth is, many people who see a psych don't "need one", they just want to talk/want help. She sees him now, perhaps for the first time as really really out of touch, shockingly out of touch.

This is again verified in the car when all 3 are driving in the cop car, Linda in the back (I'm probably over-quoting, but it all fits)

Luci: Oh, well, I hope our case didn't ruin your kissy-time with Dan.

Chloe: What is with your recent obsession with my love life?

Luci: Obsession? (laughs) That's awfully defensive. Probably indicates deeper issues, wouldn't you say?

Linda: I agree. Why are you so defensive, Lucifer?

Chloe: Good question.

Lucifer (the title of the episode): Et tu, Doctor?

Linda: Lucifer, you asked me to analyze the situation.

Lucifer: No, I asked you to help figure out what's wrong with her (Chloe).

Chloe: (gives Lucifer a suspicious look) Did you now?

Lucifer: (realizes he shouldn't have said that in-front of Chloe) But...

Linda: Nothing's wrong with her. She's a woman balancing a lot on her plate, and, as far as I can tell, doing a fantastic job.

Chloe: Why, thank you.

Linda: You're right, Lucifer, she's amazing.

Lucifer: No, she's verbal Ebola. Where's the button to put the glass up?

Chloe: This isn't a limo, Lucifer. And, Dr. Linda, you should really join us more often.

Lucifer: (scoffs, sighs) Getting double-teamed is usually much more fun than this. Mm.

Chloe: Gross.

and after they stop, Dan drives up, gets out of his car, Linda sees Dan for the first time, Chloe walks over to talk to Dan about the Palmeto case and about Malcolm.

Dr. Linda: So that's Dan, huh?

Luci: Yes. Numbingly average, isn't he?

Linda: I wouldn't say that.

Lucifer: What... You're supposed to be on my side, you know.

Linda: No. I'm supposed to help you process your emotions so you can deal with them constructively.

Lucifer: Yes, by being on my side and realizing that I'm right.

At this point, Dr. Linda looks like she's working on a response to Lucifer's pathological selfishness, but he stops her, picks up a flyer from the car and says (paraphrasing) "I have to go see these group therapy people", hands Linda the flyer and walks away.

So, at this point, Dr. Linda has seen how he is with Chloe and had a conversation with him about Chloe and she's convinced Lucifer is pathologically selfish. (there's probably a real term for that), but she's stunned by how out of touch he is.

Scroll forward, Chloe & Linda talk alone after the arrest of the 2nd suspect.

Chloe: And once again, Lucifer disappears.

Linda: I think the case may have hit a little too close to home.

Chloe: Maybe things got a little too boring for Mr. Short Attention Span.

Linda: I don't know. He's grown quite a bit since working with you.

Chloe: I'm not sure I'm the reason. I think you've really helped him. I underestimated you before. I'm sorry.

Linda: Not needed. But thank you.

Chloe: And I thought (chuckles) ... I thought you were sleeping with him.

Linda: Oh, I am.

Chloe: Oh. Oh. Is, um... is that...?

Linda: Ethical? No. (emphasis on 2nd no), No, it is not. (sighs) (and in almost a whisper): But there's something about him. ... (back to normal voice) I can't stop myself. (chuckles) (sighs) But I think it's time I did. I mean, even I'm starting to feel... (then Linda changes the subject), So do you think she did it?

and finally when she ends it:

Lucifer knocks on door

Linda: Uh, come in.

Luci: Hello, Doctor.

Camera shows Linda, not turning around right away, first she takes a deep breath and sighs, readying herself for what she knows she has to do.

Linda: Thank you for coming. Uh, I know we're not due for a session for a few days.

Luci: No, my bad. I realize I'm not up to date on my payments, so... (chuckles)

Linda: Uh... don't.

Luci: What's wrong?

Linda: Nothing's wrong. I realized a few things. As I said, we made a breakthrough. And I think, with that in mind, we should keep our relationship professional from now on.

Luci: Oh. Are you sure?

Linda: Very much so.

Luci: Very well. If, uh... if you think it's best.

Linda: I do.

Luci: Right. Well, I'll, um... see you at my next session, then.

So, the reason is pretty clear. She's a good doctor and she takes her work seriously. Unlike Chloe, who suspects Lucifer might not be human, though she's not sure what to think, Linda has never seen Lucifer throw someone 20 feet through a window. She's never seen his devil image in a mirror or, when she was shot, think she saw him get shot but not get hurt. Dr. Linda has no inkling that he's the devil, she thinks he a man who really needs help and she has a duty to that. (real ethics would suggest she refer him to someone else, but we're asked to overlook that in the story), but even with seeing him as a man who needs her help, and the ethical issue with sleeping with him, it's still hard for her to say no more sex.

I don't think Amenadiel had anything to do with it. He wouldn't care. In fact, she seems to resist his inquiries in discussing Lucifer with him as well. The force is strong with Dr. Linda, so to speak. I mean, she's not a jedi like Chloe, but she's no pushover. She has a mind and a will of her own, demonstrated by not letting Lucifer have the files he wanted and by not agreeing with him and it was also demonstrated when she met Maze in the bar for the first time and Maze insulted her and she stood up to maze, saying "people who insult feel out of control", Maze walked away after saying "I like you". Maze didn't see the Dr as nearly the threat she saw Chloe as, so she wouldn't have stepped in and influenced the Dr. to stop the sex. She might have wanted to stop the therapy sessions, she wouldn't have cared about the sex.

Did Chloe's presence influence her now that season 2 has revealed that Chloe is special? Possible, but it was still clearly a realization that she had to do it, and a conclusion that she reached based on her own ethics. It was very much a choice she made, not something that was forced upon her. The script leaves little doubt.