Why does Lefty say that he has to "check his lipstick"?

When Lefty is in the car, he is indeed afraid of being "whacked". He's checking his mirror to see the back seat of the car, so he can keep an eye on everyone in the car and be ready for anything (in the hope he could do something about it).

We can see his fear from the script:

SONNY Hey, Left, what'cha doing?
LEFTY Just checking my part.
SONNY (chuckling) - Ah, Left--what am I gonna do without you? (to Donnie) What would you do without this guy, hah, kid? You'd have to find yourself a new goombah.
Lefty getting VERY NERVOUS...
NICKY That was something about the boss, wasn't it?
SONNY We all gotta go sometime.
Lefty, TERRIFIED, looks at Boobie again. Boobie nods. Donnie WATCHES this...
Thinks: what to do?
They walk from the parked Mercedes toward a FREIGHT HANGAR. The scene is otherwise DESERTED. Lefty NERVOUS, lights a cigarette. Planes periodically ROAR overhead.
NICKY (sings) 'Love on the rocks, ain't no surprise.'
LEFTY Sonny, what is this? we glomming something?
Sonny opens the door.
SONNY After you.
Lefty walks into the DARKNESS...A terrifying SILENCE...Then-- RRRRRRROAR
The LIGHTS come up. A pale and shaken Lefty looks straight into the eyes of a LION CUB as it GROWLS. A bluff FREIGHT HANDLER holds the lion on a leash.
LEFTY Christ. I think I shit my pants.
FREIGHT HANDLER It was supposed to go to some animal dealer. Fuck him. I'll tell him it got lost.
SONNY Look, Left, he likes you. The cub nuzzles and sniffs at Lefty.
LEFTY (to Lion) Get the fuck outta here.
SONNY That's for you, Left. For your birthday. Batter late than never.
LEFTY That's why you sent for me?
SONNY Yeah, why? Whaddayou think, you was gonna get whacked? (laughing) Lefty thought he's gonna get whacked!

On an interesting side note, the scene you reference isn't in the theatrical version of the movie, but on the director's cut, as can be seen here.