Battle frontier
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Lugia learns Sky Attack at level 99.
You can teach it that in the battle frontier in HeartGold and SoulSilver OR breed it Sky Attack.
There is only one way . youre Pokemon has to learn it at a certain level . there is no TM for sky attack.
Articuno is not able to learn the move Sky Attack. It can only be taught Sky Attack with the TM 43 in Pokemon Red and Blue. Sky Attack is no longer TM 46 in later games so it's impossible for Articuno to learn Sky Attack outside of Pokemon Red and Blue.
Faint attack isn't a TM, so you can't find it anywhere.