Ok, I see now. Is the TV going to be only mounted to the wall, and the panel will be completely separated? That would be optimal, as you could just back the panel up a foot or two if you find the TV to be too big. Sounds awesome.
Lag is a problem, but if you can find something that's listed in that I linked to you'll be safe. For example, the 50 inch Panasonic TX-P50S20B has 16ms of lag, which isn't bad. 1 frame at 60Hz is 16.67ms, anything under that is pretty good for a flat screen.
The only challenge is finding something on that list that you can find in the store right now. Go through the models, and if you're lucky you'll find something. If not, read how to measure input lag, and go to the store and do some testing for yourself.
The last thing is that these classic arcade games ran at about 240p, so they're going to look really ugly and blocky when blown up on a huge 1080p tv. It sounds like you could use MAME's new HLSL effects to fix this pretty well by giving it a simulated CRT look.