Cathy,
There is an exception - sort of. My Aldens Magic Zig Zag is a left homing machine and it has a LMR lever.
Here's a pic:
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The straight stitch foot and needle plate:
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The weird thing about this machine is if you leave the ZZ needle plate in, you can put it on M and have a center home machine. But, put the SS plate in and it becomes a left home machine.
Weird. I just leave the ZZ plate in it.
Joe