He never does.
Luxray is a physical attacker, why on earth would you want Hyper Beam on it ??
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Gyarados learns Hyper Beam at level 50.
Thunder(Tech machine) Thunder fang bite hyper beam charge beamLuxray can learn thunder fang at level 42, discharge at level 56, scary face level 49, That is all I can remember and having my luxray take in. I beat the elite four with him and my starter only.
level one hyper beam
Luxray does not learn charge beam by itself, you must use TM57, which holds charge beam, on your Luxray.
he learns it at level 56