David Lee is on this team to be pumped up and dumped off to the highest bidder, or barring that allowed to quietly expire. He's not in our long- or medium-term plans no matter what happens. So in the unlikely event he has a monster year, we'll probably start looking to trade him to a contender ASAP.
If David Lee has a monster year, the team might be close enough to looking like a longshot contender that Ainge looks to acquire someone.
I think there is a non-zero chance that Lee is a Celtic in 2016-2017.
I think we'll be looking to acquire someone regardless of how we do this year - the 2016 offseason seems like the dropdead date for at least moderate roster consolidation, otherwise we'll have like 18-20 roster-worthy players to sort out. So we'll almost certainly be looking for moves, though of course it's a lot easier to look than to find.
In addition to being far older than the rest of our rotation, Lee is our biggest expiring contract, which is also why he'd be a logical guy to try and deal this season (though again if he expires and signs elsewhere that's also one more free roster spot for next year). He'd have to be playing at a pretty amazing level for us to forgo that to try and contend right away. Not impossible, but not very likely.
I agree there's a non-zero chance he stays with us after this season, but that isn't really saying much either. If you had to bet on him resigning here I'd imagine it'd take some pretty good odds to do it.