Dragapult is a pseudo legendary Pokemon so it should be able to take some hits.
i think that Lucario/Mega Lucario will take care of Dragapult.
Steven’s Metagross was also a Psuedo Legendary and was his ace and was able to Mega Evolve and yet despite all that Ash’s Dracovish did enough damage to his Metagross that he decided to recall it instead of having it try to beat Dracovish.
Likewise during Ash’s battle against Cynthia, Cynthia chose to simply recall her Garchomp after it set up Stealth Rock instead of trying to have it take out Dracovish.
Also no, it’s pretty safe to say that Lucario/Mega Lucario is not going to be the one to take out Dragapult do to simple fact that the only move it can use to damage Dragapult is Bullet Punch and on top of that it’s entirely possible and likely that Dragapult has its ability Cursed Body.
If any Pokémon is taking out Dragapult it’s going to be Dragonite or Dracovish but given the situation it’s pretty likely that it’s going to be Dracovish.
Also may remind you of the fact Iris’s Dragonite being a Psuedo Legendary didn’t stop or prevent it from losing to Dracovish relatively quickly once it was in Dracovish’s jaws.
Considering that Dragapult is in the worst possible situation against Dracovish here in that scene Dragapult being a Psuedo Legendary Pokémon isn’t going to really matter or do that much to protect it from Dracovish.