[Pokey]

LAG raises 25% of the hands he sees, so neither a king nor an overpair is a guarantee for his hand. His aggression means that he's going to bet like this whether he's got you dead or not. In this case, you're in "way ahead / way behind" mode: if he's got a better pair, a K, a 9, or a 4, you're dead. All of these holdings are possible. If he's got anything else, you're way ahead.

I'm not sure you win 2/3 of these hands, so I don't really like a raise anywhere. I am sure you win enough times to make calling to the showdown profitable.

The only place where I MIGHT have raised this is pre-flop, since a pair heads-up against a LAG has some good value in it, but checking is also fully acceptable. Given that you checked pre-flop, I don't see any need to raise unless/until I improve to trips or better.

Nicely played.