LAP would be fine! Leo is nice and goes well with Oscar.
My friend had a hard time naming her daughter...she really wanted to call her Grace Allison but the surname started with a G so she would be GAG. We told her is was better than naming her HAG or VAG. She ended up using Grace Allison in the end anyway.
Leo is nice, goes well with Oscar. With the initials AP you'll have trouble not forming a word - SAP, CAP, GAP. It doesn't matter, might make his friends at school giggle once maybe? But it's not a problem for most robust kids. Not like you're planning to call him Gaylord (cue Offended mother of Gaylord popping up on thread)
My vote is for Milo. Not as popular as Max and goes really well with Oscar. I think it works well with the middle names too. You will rarely say the first name and middle name together anyway, so wouldn't choose a first name on that basis.