Lore-wise, how is aura sphere a fighting type move if other pokemon besides Lucario (Togekiss, Clawitzer, Zeraora to name a few) can also learn it? And why is aura wheel electric?
Well, Aura Wheel is a different thing from Aura Sphere, because if you go back to the original Japanese, the “Aura” of Aura Wheel is オーラ, ōra – just the English word “aura” written in katakana. This is, I have to assume, a reference to the new-age/pseudoscience concept of auras, visible, colourful energy fields that represent your personality or mood (which is why Aura Wheel changes type according to Morpeko’s mood). The “Aura” of Aura Sphere, also mentioned in Lucario’s flavour text, is はどう/波動, hadou, which means something like “wave energy” (see also the classic Street Fighter move Hadouken, or “Wave Motion Fist”). Despite the English translations, the two are completely unrelated.
As for the other Pokémon that learn Aura Sphere – the move is supposed to represent, basically, weaponised spiritual energy (it’s… well, it’s a Dragonball Z ki blast; there’s no other way to put it). Lucario gets it because of the mastery of spirit produced by intense martial arts training. Other than Fighting-types, it’s primarily learned by Pokémon with what you might think of as “strong souls”; Togekiss, Mewtwo, the Sinnoh space-time trio, Magearna. Clawitzer and Blastoise, on the other hand, get it because of their Mega Launcher ability, which powers up things with hadou in their Japanese names (the “Pulse” moves).