You do not need Surf to reach Lavender Town. You can access Lavender Town by travelling north from Fuchsia City. There is a path leading directly to Lavender Town, and you don't need to use Surf to get there.
However, you will need Surf to explore other areas later in the game, including the following:
* Reaching Cinnabar Island: You need Surf to get to the island where you find the gym leader Blaine.
* Exploring the Seafoam Islands: You'll need Surf to traverse the islands and challenge the gym leader, Blaine.
* Finding rare Pokémon: Many rare Pokémon are found in the ocean, requiring Surf to catch them.
So, while you don't need Surf for Lavender Town, it's a vital move for progressing further in the game.