Lynn kissing Lincoln, -then- almost killing him with a Dutch oven. Now that would be in character.
Actually I suspect that the cause of Lynn's and Lucy's argument will be what Lynn ends up revealing to Lincoln in an unusually candid moment for her.
My bet is all of the sports, and its underlying competitiveness, is the result of Lynn trying to distinguish herself from the rest of the Loud girl pack. Imagine being the fifth sister of a family and going through school and being constantly compared to your predecessors - it would weigh heavily on anyone who hadn't established their own social identity yet.
Of course I could be totally off, but it's a reasonable assumption that Lynn's always-on competitive nature might rub Lucy the wrong way, forcing the argument. Having Lincoln be Lynn's confidant about her need to stand out - and the fragile nature of always needing to succeed - might give him the chance to show her she can be okay with not always being the best, and that she's just as unique in the family as everyone else.
Heartfelt moment, -then- Dutch oven to neutralize the sappy feelings without hurting the underlying message.