This is actually not true. Depending on the levels of your Tyranitar, either Bite or Smack Down wins out due to break points.
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If it's Partly Cloudy, then certainly double rock. But otherwise it goes:
Smack Down + Crunch
Smack Down + Stone Edge
Bite + Crunch
Bite + Stone Edge
Source = Pokebattler.
The reason being that all the moves are good against Lugia but SD is the better Fast Move and Crunch is the better Charge Move.
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I think they are all very close, just go with what you have powered up.
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Thanks,
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If you have them with the same strong, I would use the dark set normally (because it's easier to avoid Lugia's charged attack) and the rock set when the weather givs it more power. With normal weather, both sets have the same DPS against Lugia
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If partly cloudy, use the SD/SE moveset.
If foggy, use B/C moveset.