The Vs. Seeker doesn't work in caves, unfortunately. The best place to train is in Victory Road.
-However, it *IS* Possible to win with the current team, provided you're careful. Teach Zapdos Thunderbolt, and it'll have little problem defeating Lorelei if it's at level 55.
-Use Articuno's Ice Beam on Bruno's Onix and Zapdos's Drill Peck on the fighters, using Charizard's Wing Attack (if you have it) on anything that gets by.
-Agatha would be a challenge, though, so just use Charizard and blast your way through with Flamethrower. Switch to one of the lower level Pokemon as a shield if Charizard faints and recover it while letting the weaker Pokemon take the damage.
-Lance should be easy. Just have Zapdos thunderbolt Gyarados, and then Articuno will sweep the rest with Ice Beam. Watch out for Aerodactyl, and use Zapdos for that. Hopefully it won't faint, but Lance's AI is rather... bleh.
-The Rival will be a little tricky. Start off with Zapdos and thunderbolt the Pidgeot. It'll probably waste time with Feather Dance. Ice Beam Rhydon and use Charizard against the incoming Fire-type. Use Zapdos against the Water-type (hopefully you haven't run out of Thunderbolts or you have some Ethers/Elixers), and either Charizard or Articuno against the Grass-type. With Alakazam, just use Charizard's strongest physical move, and it should be down with one hit.
Good luck. Be sure to pack lots of Full Restores, Hyper Potions, Full Heals and Revives.