Metagame issue: cap a LAG who is in bb, when we're in position?

[Wynton]

In another thread at HUSH, I asked about capping with A10 from MP after an aggressive player 3-bets you from bb. See here.

I'd like to get more discussion about the metagame benefits of capping a LAG, when in position. In other words, I raise from MP, and the LAG 3-bets from the BB. (I'm excluding sb, because I think that's an entirely different situation.)

What hands would you cap with in this scenario? Should we be liberal about capping, because there is a decent chance the LAG is on a worse hand range than us in the first place? Or is that fact actually an argument for just calling, so that we can retain flexibility about either letting LAG keep firing away and/or abandon the hand more easily ourselves?

Aside from that particular hand, is capping good because we want to discourage LAG from 3-betting in the future? Will we discourage him more if we just call and raise a subsequent street? Or are we better off encouraging the LAG to continue overbetting future hands?