At our school, the staff lounge is exactly that - a staff lounge. Volunteers, PTA or not, don't go into the staff lounge. I don't think this is a "rule," however it is a common courtesy for us. Even I don't go into the staff lounge unless it's after hours...not only am I our PTA President, but also the husband of one of the teachers, and I see many of them outside of school hours, so I'm sure they wouldn't mind, but it's just common courtesy on my end!
Teachers go into the lounge to relax and to take short breaks and lunches. There are conversations that are of a personal nature that go on in there, not to mention discussions about students that should not be shared with or overheard by parents.
I think you should respect the teachers' privacy and find another area to do your own lounging...or whatever it is that is taking you into the lounge.
As far as the equipment, I agree that you everything you do is for the school, whether or not you feel PTA/PTO owns the equipment. When your group purchased the equipment, I'm sure it wasn't with the caveat that you would be able to use it...it was for the benefit of the school.
I'm sure your volunteers spend a lot of time at the school, however is it really necessary for you to use the equipment? Can it wait until you got home to eat lunch? Most teachers don't have that luxury.
With all this being said, however, have you tried working with the school administration to try to use the lounge during times when the staff isn't in there? There have got to be plenty of times when there aren't teachers in there.
I'm sorry I'm coming across a little hard, but these are exactly the things that ended up ruining a relationship between PTA/PTO and teachers, and without their support, you have almost nothing. A lot of people forget what the "T" stands for in our organizations! At our school, we are lucky that we have a lot of teachers volunteering to do things for us, like running family nights. Over the last 5 years that my wife and I have been involved, we've had several teachers on our board (including my wife who is a teacher/parent at the same school).
P.S. - When I say "you," I'm referring to the people on your board that are having a problem...it's just faster to type!