The Zoo proper is posted.
The parking lot might be; I do not remember seeing such a sign the last time I was there (a couple of weeks ago.)
I carry, park, lock my pistol in the car, transition to the Zoo, see the sights, return to car, unlock and rearm, then leave.
I will say this: I feel much safer in the new parking lot than the old system where you might be caught idling on Drury, or take a chance parking on the public street. Plus the new lot is almost fully shaded by the solar panels, so the car is usually cool on return.