It actually got worse with the Dodgers, he just had great BABIP luck that masked it:
CWS Lance: 5.19 FIP, 10.8 K/9, 3.20 K/BB, 2.1 HR/9
LAD Lance: 6.16 FIP, 6.6 K/9, 2.14 K/BB, 2.3 HR/9
Whatever they tweaked to try to make him better against lefties just got him crushed by righties instead. It took Lynn 278 ABs vs. RHH to give up 10 HR as a Sox (3.6% rate), and just 129 ABs to do the same as a Dodger (7.7% rate) despite a less HR friendly home park.
But he had much better luck on the balls that stayed in the ballpark (his BABIP dropped by nearly 100 points to an unsustainable .232), so he avoided the "big" homers en route to giving up more overall.
Hopefully the Cards have a different plan than LA, because his contact profile there wasn't encouraging at all for a guy whose biggest problem is the long ball:
GB%: down 6.2%
FB%: up 7.6%
K%: down 9.7%