Alitalia LAX-FCO-Germany.
You might be able to find availability on dl.dumb and those are the best beds across the Atlantic.
Why people keep pushing AA with substandard products and BA fees.
LX is a decent backup plan, but good luck finding availability.
You can book AF easily with MR but you'll pay feeeees.
Nothing will come easily in summertime.
Deltahater's point is a valid one - I regularly fly to DUS for work in Holland