Jolteon is plenty good enough for Lorelei, KO'ing Dewgong and especially Cloyster without trouble. Lapras might be tougher to KO because it can surf right back, but if you want to be safe, Heracross should be enough with Brick Break. Assuming it outspeeds Jynx, Megahorn ruins Jynx, though I'd say Tyranitar or Charizard have that covered nicely. Piloswine also goes down to Heracross easily.
Bruno is exactly what he was last time except Steelix is around, meaning Charizard takes them down easily. If Charizard knows Fly, that should go smoothly, but with Rock Slide around, you may want to consider a Psychic type, since they work best against Bruno. Alakazam works, but I prefer Starmie for its better physical bulk to handle Agatha. If you don't mind a slow Pokemon, Slowbro works, though it would require trade. Still, any of them should work to beat Bruno.
Agatha is handle pretty well by Psychics, if you choose to add one to your team, though Tyranitar is more than good enough for this fight. Crunch for the ghosts and Earthquake for Arbok should make this fight a simple one, though Jolteon should be able to handle Crobat on its own. Not much else here.
Joteon destroys Lance's lead, Gyarados, and can take out Aerodactyl as well, though Blastoise is better suited for that one because of Jolteon's weakness to Earthquake. If Blastoise knows Ice Beam, the weaker Dragonite is no problem, and if it's strong enough to take a Thunderbolt, the other one should go down as well. That still leaves Kingdra, who is only beat by Dragon moves. Your own Dragonite could work here, but Dragon Dance and Ice Beam are a problem. Blastoise may be your best bet here, because his only way to damage it significantly is Hyper Beam, which is an awful, albeit strong move.
As for the Champion, Heracross and Venusaur/Exeggutor are no problem for Charizard. Alakazam stands no chance against Tyranitar, and his Tyranitar is taken down by Heracross. Careful with Aerial Ace, though. Gyarados/Blastoise is no problem for Jolteon, but if he has Blastoise, Earthquake is an issue. Heracross and Blastoise aren't a bad option either for Blastoise. His Arcanine/Charizard is no problem for Blastoise or Tyranitar, so that's no problem here.