LH & EK have interline agreements, but I doubt SK (who handles LH in OSL) will check you thru at the first request. Their policy on separate tickets is very picky. You can try, but no guarantee. If tagged thru, LH will transfer the luggage to EK in FRA.

Take a look at the SAS Eurobonus forum on Flyertalk for a few hints on the topic.

PS welcome to FT!