KK against a LAG on an ugly board

[spacemonkey57]

Villan is a super LAG 83%/38%. Anyone playing this different? Bet the river or is the ace and the double paired board reason enough to call down. I don't think he's got a Jack or a three, but he may have an ace and even lags have good cards every once in a while.

Party Poker 1/2 Hold'em (10 handed) converter

Preflop: Hero is BB with K[img]/images/graemlins/heart.gif[/img], K[img]/images/graemlins/club.gif[/img]. CO posts a blind of $1.
<font color="#666666">1 fold</font>, UTG+1 calls, <font color="#666666">4 folds</font>, CO (poster) checks, <font color="#666666">1 fold</font>, <font color="#CC3333">SB raises</font>, <font color="#CC3333">Hero 3-bets</font>, <font color="#CC3333">UTG+1 caps</font>, CO folds, SB calls, Hero calls.

Flop: (13 SB) J[img]/images/graemlins/club.gif[/img], 3[img]/images/graemlins/diamond.gif[/img], 3[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(3 players)</font>
<font color="#CC3333">SB bets</font>, <font color="#CC3333">Hero raises</font>, <font color="#CC3333">UTG+1 3-bets</font>, SB folds, <font color="#CC3333">Hero caps</font>, UTG+1 calls.

Turn: (11 BB) J[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets</font>, <font color="#CC3333">UTG+1 raises</font>, <font color="#CC3333">Hero 3-bets</font>, <font color="#CC3333">UTG+1 caps</font>, Hero calls.

River: (19 BB) A[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#CC3333">UTG+1 bets</font>, Hero calls.

Final Pot: 21 BB