Lt. Surge uses electric Pokémon. As I mentioned earlier in Misty's page, electric has an advantage over water. So you might not want to bring your Wartortle(if you chose Squirtle) in since electric moves can probably KO Wartortle. I think Bulbasaur might be a better choice here(since electric has a disadvantage over grass, I think). Charmander is a good choice too.

However if you have picked Squirtle in the beginning, you might want to try Diglett's Cave on the way to Route #11. Digletts are immune to electrical attacks.

I find Lt. Surge's gym very annoying since you have to find switches to open the doors. The switches are hidden under garbage bins so if you found one, the second one is nearby(BTW, there are two switches). If you didn't find one, the switches will switch to another garbage bin and so forth.

Be sure to bring Paralyz Heals because electric attacks can paralyze your Pokémon(yick).

If you win, you gain the Thunder Badge, which increases your Pokémon's speed and allows you to use HM02, Fly anytime.