There aren’t that many Electric-types to choose from, so this shouldn’t be a difficult battle if you came prepared. 
Voltorb can use Light Screen to halve special-based attacks for a few turns. Most Ground-type moves are physical, so no sweat.
Magnemite is an easy win for a Ground-type. But if you want to let them relax for a bit, you can switch in a Fire or Fighting-type instead. But only if your Battle Style is Switch, unless you’re a masochist.
Finally, we have Lt. Surge’s famous 
Raichu. Please resist the urge to send out 
Pikachu like in the cartoon. Actually, if it’s your partner Pikachu, it could probably handle it. But a regular Pikachu is going to struggle.
Instead, we suggest a reliable Ground-type. That way, Raichu will be stuck using weak moves like Quick Attack and Double Kick. You’ve got loads of options, from 
Geodude, 
Onix, 
Diglett and the fully evolved Nidoran.
Survive Lt. Surge’s shocking assault and he’ll hand you his Thunder Badge plus his Autograph. So how much can we sell this for? Oh, he’ll also give you TM36 Thunderbolt. If you didn’t get the chance to see it, it’s a very strong Electric-type move.
That’s three Badges under your belt! When you leave the Gym, you should see Misty standing by the Poké Mart. She’ll offer to lead you to Diglett’s Cave, towards the east of Vermilion City. Refuse or not, you’ll want to go there if you want to make progress.
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