Lillehammer is a city in Norway.
If you're heading either North or South there are two places, as far as I know, that you can hitch from.
If you've hitched in Norway before then you probably know that asking people for rides at gas stations is the way to go.
There is a "Statoil" down by the lake close to a shopping mall called "Strandtorget". Some people stop there if they're going to Trondheim or Oslo.
The same goes for an "Esso" a bit further North. I haven't hitched from the "Esso" gas station before, but it's probably just as good if not better. The "Esso" is close to a furnishing store called "Skeidar" and a "Marché" restaurant. If you need directions, locals should be more than happy to help.
Lillehammer is a tricky place to hitch East from. There aren't too many roads that go East and people don't usually drive eastward from Lillehammer.
Places to avoid
Lillehammer is really peaceful. Beautiful scenery and nice people. As far as I know there aren't really any places in particular you need to stay away from.
Accommodation and Sleep
"Strandpromenaden" is a nice spot to camp by the lake, just south of "Strandtorget". Be wary of rain, there isn't really any shelter there. Another similar spot is the beach close the E6.
None of these places are actual camping sites, so I'm not sure whether or not it's legal to camp there, but just staying there overnight shouldn't be a problem.