Currently the relationship is that Lufthansa own a chunk of jetBlue. That's all. No earning and no redemption betwrrn the two. There are some
pretty strong indications that the program is going to improve, including LH relationships, at some point in the first half of the year, but no real details have come out yet. There is a chance that some things will come through for you by late in the year, but I wouldn't bet on it working out great at this point.
The AerLingus partnership is pretty poor, also. It basically allows you to connect betzeen the two carriers and (I think) get the trip issued on a single ticket, but no cross-earning or redemptions are available.
Right now jetBlue is somewhat of an island with regards to airline partnerships.