Me and my two brothers play three player battles every now and again.
We use a system I half stole from DC Hobbit League's Chaos in Arda but it works really well.
Basically put a central objective (tower, fountain, statue) on the board.
Take turns to deploy a warband at a time, anywhere on the board outside of 6" of the objective and any enemy model.
Draw three cards from this deck (
https://www.mediafire.com/file/rwua8iv1 ... attles.pdf). Players can cash in the cards once complete for the victory points on the card. They can trade or swap one card out each turn but must let the other players know.
You'll have to make some stuff up as you go and it's version one but so far it's been some of the best games of lotr we've ever had.