Since my NME modded 360 is no longer be able to play new Ap2.5 games I am thinking about flashing it with LT+ in order to be able to play Ap2.5 protected games.

However, I was wondering if this is even possible since my box has already been modded with the NME chip. Will the NME chip still work for all of my older games if I flash with LT+?

any chip is uneeded for any lt drive bin the chip they are pointless and I would say that if anything lt is a dam site safer then a chip at present ..

What would happen though if I kept my chip installed but flashed the drive so I could play new games? Would my chip still work allowing me to play my old games that were NME Patched?

No. Just re-rip the games from your originals to make normal backups.

I still have a NME chip and it works with all games to date never had a prob. My flashed xbox is a backup that sees very little action and my jtaged box gets no play at all. My NME compatible backups work on all three systems.

Ditto. Thus far everything seems to work on my NME2 box.