That depends on a number of factors. The primary cause of "skunk" is sunlight interacting with the delicate hop oils. So the more you can shield your brews from sunlight, the longer they'll last. Also, the higher the gravity/ABV, the longer they'll last.
With that American Lager, well, I don't know the OG on your recipe, but lagers, in my experience, are very quick to skunk out. So keep it hidden from sunlight, and don't count on it lasting as long as, say, the Guinness clone you're planning.