Can I season cast iron *without* using an oven?

Lodge claims their pans are pre-seasoned. It's a great company, but don't believe that pre-seasoned malarcky. Yes, they do treat the surface with oil, but not nearly enough. No worries though, you really only need a good seasoning layer on the bottom, cooking surface.

Scour the cooking surface of the pan thoroughly, then add a film of oil to the bottom of the pan and heat it on a burner. Move it around frequently to minimize hot spots. Let it get to smoking, allow to cool enough to touch, wipe it out, and then a add a bit more oil and smear it with a paper towel. Repeat 3 or 4 more times. Ignore the walls and handle of the pan for now, just thoroughly re-season the whole thing when you have access to an oven.

Opinions vary as to the best oil to use. My personal favorite is lard, flax seed is often highly recommended.

Read this question and answers for more info: What's the best way to season a cast iron skillet?

Congrats on your new pan. Cast iron is lovely, I have a set of skillets that belonged to my grandmother, my mother and now me. Cast iron takes some "getting to know" but once you know your pan you'll love it. BTW, except for the first time scouring, ideally your pan should never see soap or detergent. There is a lot of good info here about cast iron, just use the search engine to learn more.

EDIT: One more thing. All new cast iron pans are treated in some way before they are sold to prevent rust. In the case of Lodge, that treatment is a light seasoning with food grade oil. There is nothing that needs to be removed before first use. In fact the seasoning step I recommend here in not technically necessary, it just gets you to that black, old, almost-as-slick-as-teflon surface faster than repeated use alone. I only recommend scouring the cooking surface before you season the first time to give the factory surface a tiny bit of "roughening up", giving your first seasoning layer a bit of something to grip on to. So don't scour the whole pan, just the cooking surface. By the time you have access to an oven, the factory surface on the rest of the pan will already have developed some patina just from use, so you don't need to scour to season the rest of the pan, just oil the whole pan.

Some cast iron pans from other companies are not preseasoned, they're coated with wax or some other thing you don't want in your food See: Do all new cast iron pans and skillets have a protective coating on them, which must be removed? Those pans have to be scoured all over before first use. Ideally, then they would be seasoned in an oven before first use. If you had a pan like that, but no access to an oven, my advice to you would be the same accept that you would need to scour the whole pan, season the cooking surface and lightly oil the whole pan every time you heat it for the first several times, periodically thereafter.