As far as mods go, you'll want to go with +Luck to fix up Arthur's Luck for Lutz. Your flaw could be pretty much anything bar Strength or Defense, depending on what you want Lutz to end as.
For secondary class, he can run a Pavise/Aegis set if he buddies Benoit/Benny. Looking at his mods and growths, I think you might want to give him Samurai for Weapon Master (and therefore Line of Death). So far, seeing as you also want to have him be a Vanguard, I'd try:
Pavise/Aegis/Line of Death*/Aether (from Vanguard)/Defender
Your end class can be anything seeing as +Lck gives +2 to both Str and Mag.
*You can also run Lancer and replace Line of Death with Flamboyance