I used to fly Spits a lot. I always saw LA's as a lunch treat unless they ran away.
I've been flying the LA-5 and more recently the LA-7 a bit and here's what I've found; Keep them low (under 10K) and fast. Against turn fighters use them in a slashing role (attack, extend, turn, attack). Keep convergence under 400 as ballistics aren't that great.
Used this way they can beat just about anything.
They will, of course, out-turn a lot of planes but not the best turn fighters and they will B'n'Z and extend pretty well but not as good as the best B'n'Zers. They really fit into that middle ground so many of the planes in the set do although, like the Spits, they are at the upper end of that middle-ground. While the Spits lean toward the turn fight the LA's lean toward the B'n'Z role although both are pretty good at both styles of fighting.