Quick Claw has a 20% chance to allow a move to go first in its priority bracket.
So Quick Claw does not give you +1 priority, it simply allows you to go first in its own priority bracket.
For example, if Quick Claw activated when you used Tackle(+0 priority) and the foe used Drain Punch(+0 priority), then you would go first. However, if you used Tackle and the foe used Extreme Speed, you will go last even if Quick Claw activated, and if you also used a +2 priority move, then you would go first.
So even if Luxray used Roar(-6 priority), it would still go last, unless the opponent also used a move with -6 priority.
I assume you were confused because Luxray went last even if Quick Ckaw activated.
If you are confused because Luxray used Roar, it can learn it at level 23.
Source: Experience and this