I think generally speaking cold 4-betting to broke PF is the best.

IMO is more interesting thinking about how the LAG 3-bettor reacts, since:

1) If he starts realizing that we are capable to cold 4-betting him, he can not be able to 3-bet that lightely anymore when we are behind him, but

2) If he's aggressive and overextimates our frequencies (maybe thinking we are cold 4-betting a blocker hand in bluff too often) he may push with hands like AJ/AQ

In order to let him think so, of course you have to start cold 4-betting also your top range in this situation, IMO.
Obviously I am never folding against OR QQ+, even if I am not the happiest person on planet earth when he goes all-in and I've got queens.

Have a cold 4-bet bluffing range in this spot so it's not always QQ-AA

Really how LAG is the 3 bettor? lots of people 3B a bunch in blinds vs LP steals, but rarely vs Ep opens - it comes down to what % of his range is value vs bluffs? his range makes my preflop decision here

I totally agree with the above logic with 4-betting getting it in and balancing out 4-betting range with adding a bluffing range. 

However, what do you guys think about flatting our large over pairs particularly AA-KK? Our hand is strong enough postflop and given that we are good at reading board textures and are able to fold when it's clear our hand is beat, we may be able to trap more money out of our overly aggressive opponents.