The answer to your first question is yes. There are some projectors out there that will fit the bill.
There are a few things to think about though. How big of a screen you will be working with or if it is just a wall. I assume that since you specifically state that there is florescent lighting that you don't have control over that, what about windows? Is this projector going to be moved often so it needs to be fairly portable? Is there a set budget?
If you don't have very much lighting control I would suggest trying to get a projector with a minimum of 2000 lumens. Also if you need to move around quite a bit and don't always know the places you will have to project you will want something portable with a good short throw distance.
Here is a page with a list of portable projectors that a lot of people use:http://www.projectorcentral.com/portable-computer-projectors.htm
I personally use a Casio XJ 360. It is well priced (ed. prices are around $17-1800), has a very nice zoom of 2:1 for throw range, weighs in right around 4 lbs, and at 2200 lumens it is quite bright.