Strategies
F.S. Chamber Advice
Luke's Raging Blast needs a Grass Chamber, since it gives the Arte the useful Steal ability. His Rending Thrust needs a Cobalt Chamber, since it increases the stun ability of the technique significantly.

With that upgrade, you can create a "infinite" combo, by stringing together a combo of X X X + Rending Thrust. If you can connect them together correctly, you can continue this pattern until Luke's TP runs out.

One last thing you should do is give Luke's Guardian a Cobalt Chamber. This increases the effect of the Arte, giving Luke a pseudo-Over Limit mode.

Attack Advice
Luke's unique 5-hit attack pattern ( Down + X X X ) is the highest "normal" string available to any of the characters in the game. If you are low on TP, use this attack pattern to recover your TP faster than the normal 3-hit string ( X X X ).

When attacking with Luke, do not cancel your normal attacks into Artes unless your initial string of attacks hit the enemy. His normal attacks are easier to counter, so if you cancel too early into an Arte, you will waste TP and leave yourself wide open to a counterattack. In essence, make sure Luke's initial string of attacks hit the enemy before canceling into an Arte.

Combo Examples
X X X + Havoc Strike + Rending Fang Blade

X X X + Rending Thrust + Light Spear Cannon + Radiant Howl