To unequivocally clarify:

Whether this is a one-way booking that terminates in the USA, or a return booking with a turnaround point in the USA then it is the luggage allowance of the MARKETING CARRIER of the first Journey - this applies for the entire booking.

If you are in BER for no more than 24 hours then it is a transit and the luggage allowance of the carrier represented by the flight number on you BER-LAX flight would be yours for the entire booking.

If you are in BER for more than 24 hours then it is a stopover and the luggage allowance of the carrier represented by the flight number on your LHR-BER flight would be yours for the entire booking, including BER-LAX.

If this is a return booking, irrespective of any routing on the return, whichever of the above luggage allowances qualifies will apply to the entire booking.