Why was the airlock left unlocked for Dr. Richardson?

Why would there be an air-lock in the greenhouse?

Why do you have doors between rooms, or hatches in submarines? So you can close them in case of emergency.

In this case, in a hostile environment such as Mars sealable airlocks between sections would be required as is evidenced by the sealing of the other airlock by Leslie Richardson to save the rest of the base.

Why would it not be connected to a second depressurization?

Because it wasn't intended to be an airlock to the outside, it was intended to be a door between sections.

Unfortunately, the section it was supposed to connect to was under construction and had not yet been completed. Indeed, we see the construction in the same episode.

Why would it be left unlocked for someone to simply accidentally/deliberately trigger.

It wasn't. It was locked and Paul unlocked it. I supposed you mean why was it possible for it to be unlocked in the first place.

It's designed that way. They would be no obvious need for additional security measures like that in what would be considered a secure facility.

Certainly opening the door is not something that could be done accidentally, but it's clear that Paul was under severe mental strain and basically broke down and, in a "confused" state, killed himself.

Planning to prevent deliberate suicide is chasing an almost impossible standard. Sadly, people will find a way, they'll go to extraordinary lengths to achieve their goal.