you could name your son Lucas John which sounds better, but still call him Luke.

You could also use Luke Jonathan instead of John.

I really like Luke, I'd use it. Two middle names are fine.
Luke Brennan John - I love it
Luke Winston John
Luke Taylor John
Luke Quincy John
Luke Mitchell John
Luke Talon John
Luke Matthew John
Luke Campbell John
Luke Malachi John
Luke Dexter John
Luke Connor John
Luke Noel John
Luke Dallas John
Luke Jackson John
Luke Thomas John
Luke Gabriel John
Luke Matthias John
Luke Nathan John
Luke Aaron John

Luke Alexander John
Luke Nathaniel John
Luke Sebastien John
Luke Elijah John
Luke Cameron John
Luke Riley John
Luke Aaron John
Luke Timothy John
Luke Tyler John
Luke Michael John

Oh, this is great. Thank you!
I'm liking
Luke Brennan John
Luke Alexander John

So, here's my question: What do people with 2 middle names use for their middle initial when prompted to write it?
I ask because, if I go with a name beginning with "A" as in Alexander, his initials will spell LAG! Not good.

What about these:
Luke Zander John
Luke Brandon John or John Luke Alexander and call him Luke?

My cousin's name is William Nicholas Edward and he goes by Nick. If he has to fill out papers or anything he puts William Nicholas E.