I would doubt that EI could issue a LH boarding pass. Their two systems won't communicate with one another in such a way to allow through check-in.
Usually through check in is only available if all segments are on one airline, or if the airlines share an agreement through an alliance.
Having said that I've seen strange things happen. Boarding cards for LX flights printed by BA on BA stock. Flights for BE printed by KL and flights for CX and QF come out of the SN system. So really, if it works then great, if not then nothing to get mad over.
