How do you get to gym leader jasmine in the light house?

You can't get to Gym Leader Jasmine in the Lighthouse. Gym Leader Jasmine is the leader of the Olivine City Gym in Pokémon Gold, Silver, and Crystal. She specializes in Steel-type Pokémon.

The lighthouse is located on Cinnabar Island and is home to the legendary Pokémon Articuno. There is no Gym Leader within the lighthouse.

If you're trying to find Jasmine, you'll need to head to Olivine City, which is located on the island chain west of Ecruteak City. You'll need to defeat the Gym Leader in order to obtain the Rainbow Badge and access the next part of the game.