BREAK Evolutions are treated as their own Stage of Evolution and follow the usual rules of Evolution. You may Evolve your Luxray into Luxray BREAK so long as that Pokémon hasn't already Evolved this turn. If you just Evolved your Luxio into Luxray or Evolved your Shinx directly to Luxray via Rare Candy, you'll have to wait until the next turn.
If a card effect says it can be used on Pokémon, Evolutions, Evolved Pokémon, etc. then it should work for a BREAK Evolution like Luxray BREAK. You can search it from your deck with Ultra Ball, or with Timer Ball, or anything else that can search out any Pokémon, any Evolution, etc. Most "tricks" that don't work are due to the fact that an effect works for a particular Stage. For example, Rare Candy only works to Evolve a Basic Pokémon into the corresponding Stage 2; you could use Rare Candy to Evolve Shinx directly into Luxray, but not Luxray BREAK. You can still Evolve a Luxray into Luxray BREAK even if the Luxray used a shortcut to hit the field.
I don't think it would even matter for Luxray BREAK, but it has for certain other BREAK Evolutions, is that a BREAK Evolution isn't "complete" on its own. For example, there are some very rare effects that allow you to put an Evolution directly into play, but they don't work for BREAK Evolutions because a BREAK Evolution lacks the data for Weakness/Resistance/Retreat Cost, and instead uses the Pokémon from which it BREAK Evolved.
