[name_m]Luka[/name_m] and [name_m]Max[/name_m] are perfect together! I like [name_m]Jude[/name_m] too, but [name_m]Max[/name_m] sounds better imho as it doesn’t have the repeated ‘u’ sound.
For a three syllable middle that chimes with [name_m]Harrison[/name_m], maybe [name_m]Max[/name_m] [name_m]Callahan[/name_m], [name_m]Max[/name_m] [name_m]Benedict[/name_m], or [name_m]Max[/name_m] [name_m]Augustine[/name_m]?