We have a FP Athena which is pretty identical to the Lavezzi
mainsheet, sail area and arrangement. Our mainsheet is curently 13-14mm line which incurs too much friction through the blocks and does not fit the winch
self tailer properly. We are just about to fit a 12mm mainsheet (the same as jib sheets
which use the same winch). You do not need 12mm for strength but it is a nice size in the hands.
Incidently, we transformed our main traveller car (Amiot) by replacing all the balls (130 x 8mm dia), which turned out to be a very easy job. Now it glides across with very little force as opposed to previously dgragging and kicking it. The only difficult part was removing the SS cap screws for the ned caps, used a hot air gun to heat the casting.