Does a LEGO Technic Power Functions L Motor work with a v1 receiver? I really want to know it, because then I know what motor I should buy.
Yes, they appear in combination in the 42030 and 42095 sets. The L motor only appears in combination with the V2 receiver in the 41999 and 9398 sets.
In my experience, there is a small performance loss when used with the V1 rather than the V2 receiver.
I once asked Lego support why the Volvo 42030 came with the V1 rather than the V2 receiver as depicted on the box-art and was told that the motors might damage the set when used with the V2 receiver and that hence the receiver was swapped out late in the design phase (after the box-art was already made)