Sorry, I'm going to have to vent a little here as this is a pet hate of mine...
Put yourself in his shoes, everytime he has to give his name he'll have to say "Llincoln, with two Ls" and then they'll say "Two Ls at the start or at the end?"
I think Lincoln is the only choice. If you want your child to have a unique name, choose one, changing the spelling does not make it unique, to me it makes it look like their parents couldn't spell. I personally think you'll be fine with Lincoln, it's a little trendy at the moment but it's unlikely there'll be 3 or 4 in the class.
Ok, that's my rant for the day. I actually really like both or your name choices, just don't ruin them!lol