I wasn't sure where to start with this question - searched a bunch and found some similar situations, but not identical:

I have two separate tickets booked -

FCO-FRA, cash fare purchased from LH on LH metal, in economy (can change it to business if that helps)
FRA-SEA, Condor award via AS on DE metal, in business
These are on the same day with 1:50 between flights - MCT is 1:30 for D:I on DE US-bound, in case this matters

Does anyone know if at FCO, LH will check my bags through to Seattle? I see that LH and DE have an interline agreement, but since I'm not on one ticket or even the same ticket stock for each segment, I presume it's entirely at their discretion. Does anyone know if this would work, and what I should do in advance (if anything)?