When Lucario activates its Final Smash, it will shout "Max Aura!" (はどう最大!, Wave-Guide Maximum!), then transform into Mega Lucario.
Mega Evolution is a mechanic introduced in Pokémon X and Y. Only a small number of fully-evolved Pokémon, including Lucario, can Mega Evolve, and they must also hold a special Mega Stone unique to their species. Upon Mega Evolution, the Pokémon's stats increase tremendously and can easily allow it to turn the battle around. Lucario's Mega Stone is known as Lucarionite. The Fighting type Gym Leader Korrina from Kalos in Pokémon X and Y uses a Mega Lucario, and will award the player a Lucario along with the Lucarionite prior to their Gym battle.
In Smash 4
During this state, Mega Lucario's aura attacks deal 1.8x the base damage regardless of Lucario's current damage. Unlike most transformation Final Smashes, this state does not render Lucario invincible; it will gain super armor and immunity to grabs, but will take half damage from attacks and can be footstooled during its duration. Attacks that connect with Lucario will not cause it to flinch or get knocked back in any way, but they will decrease its transformation time and cause it to transform back to normal sooner.
Mega Lucario can be affected by Super Mushrooms and Poison Mushrooms, but like all the other transformation Final Smashes, it is unaffected by Metal Boxes. Also, Mega Lucario lasts the longest of all the transformation Final Smashes when playing at normal speed, reverting back to Lucario after 14 seconds have passed.
A notable instance where Lucario can Mega Evolve is during the final battle against Korrina, the third Gym Leader, who not only gives the player one of her Lucario, but also has them battle her own one. Both Lucario can Mega Evolve during the battle, acting as the player's tutorial for how Mega Evolution works. It is also stated in-game that Lucario was the first Pokémon to be able to Mega Evolve, though this is contradicted by legends of Mega Rayquaza in Pokémon Omega Ruby and Alpha Sapphire.