I see no reason that a cast iron waffle pan should be treated differently in regards to seasoning than other cast iron. Since it won't be cooking anything with significant fat in it naturally, if anything it may be more important! Seasoning is both for non-stick reason and non-oxidizing reasons.
Season it well on your own, then use it with some fat (of some kind) very lightly brushed on to keep it well. Only brushing right before use will keep one good likely, but would take a long, long time to naturally season since a large portion of the fat will immediately get used by the food.
Cast iron gets gummy if you either 1) season with a spray like Pam consistently or 2) don't cook your seasoning long enough and/or high enough. Use a fat, bacon fat, would be great here and season away - properly. In regards to seasoning, I recommend checking out this question, as its unneeded to replicate detailed information elsewhere in the site.
All my attempts to "clean and repair" a sticky-seasoning layer have ended badly as well. I know who already snickers in the background, but my opinion is: start clean. Give the pan a lye bath and a good scrub, then reseason with a better seasoning.
"The new hotness" of flaxseed oil goes back to the fact that it doesn't go rancid easily, without heat it just dries out making a film which can protect things like wood. I bought into it, and seasoned a pan with it, and wondered why all my seasoning tries were unsucessful (I stripped and reseasoned 3 times, I think). I came to blame it on the smooth forged iron.
Then I got Cookwise and read the chapter on fats. And surprise, what does it say? That PUFA stick to everything around. (Makes sense, if you stop to think about it - those unsaturated bonds are unstable, they itch to break apart). So, when I got my next iron pan, I seasoned it with three (very thin) layers of flaxseed oil (for a solid base which will stick to the pan and the finishing layer) and then two layers of lard. After the oven, I heated it from brown to almost-black on the stove (empty).
This seasoning turned out perfect. I made crepes on it, re-oiling once every 7-8 crepes only (no fat in the batter). The pan released them like a charm. The old flaxseed-seasoned pan still sits around with some carbonized matter burnt onto the seasoning, and waits for a lye-flaxseed-lard session.
Of course, I would still take some caution with new seasoning and oil well the first few applications (I only tried the crepes after I noticed that less problematic items work great). And if you tend to often fry with the fashinably-healthy nonsaturated vegetable oils, don't heat them too much, else they could bake in a sticky-seasoning layer onto the pan. In the worst case, if you do get sticky-oil (but not carbon) buildup, try adding a new lard layer before you strip-and-reseason.
Best Answer
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.