Upon visiting Lilycove City, you discover Team Aqua/Magma blocking the way east. You have to go back to Route 122 to proceed.
Route 122 is an all-water route, so you can only catch pokémon by fishing or Surfing. When Surfing, you might encounter Tentacool, Wingull, and Pelipper. If you use the Old Rod, you might encounter Tentacool and Magikarp. If you use the Good Rod, you might encounter Tentacool, Magikarp, and Wailmer. If you use the Super Rod, you might encounter Sharpedo and Wailmer.
Enter Mt. Pyre
There are no items or trainers to be found in Route 122, so go as far south as possible until you reach a small area of land on the south side of the mountain. Go onto that land and enter the cave to reach Mt. Pyre.