I'm not claiming to be better than you but here's my thought process:

The LAG could have all kinds of hands here, some drawish, some not

Flat-calling is bad if he has a draw. He might get away from a missed turn, and you're not getting away from the turn if he hits. If his hand is not drawish, and you call, and the turn card completes a draw, that might scare him off his K-rag or something.

Also, cold-calling him tells him you mean business, since you can't expect him to believe you are calling just so you can bluff the turn. However a raise might be a bluff in his mind (not ours)