It is interesting how Lambert's poor Liiga season had him fall all the waydown to #30 OA. I think that Lambert's easily the most technically gifted player of the draft, especially in terms of skating. He could be expected to improve faster than most of his competition, and I feel that the faster and more straightforward North American play style should allow Lambert avoid getting into the kinds of situations that cause him to get in trouble.
Lambert clearly is more of a rush type player than boardwork type player, and rush type players are doing quite well in NHL(The best example being McDavid, of course). The archetype doesn't really work in Liiga, which is dominated by grinders. I think I already said it last season, but I think that for Lambert, a fast counter attacking style would work very well. Either that, or active forechecking and disruption. Anything other than Liiga's boring dead puck era grinder hockey.
Also, the reason it's said that Liiga's closest to North American hockey is because of how much it is about grinding and boardwork. It's also the most physical European league, pretty much. But perhaps that comparison is a bit outdated, since North American hockey is moving more and more towards fast rushes and counter attacks. It's more like dead puck era North American hockey than today's North American hockey.