I'm not sure about the serial numbers, but the Lisa 1 mice had a very narrow button vs the newer ones that were shared with the Mac and Lisa 2's, and also a different DB9 connector hood (no screws).
see the photos here:
https://www.worthpoint.com/worthopedia/apple-lisa-mouse-a9m0050-early-013519-1863798648
There's a few of these on ebay that are super expensive as well.
There is a formula for the serial number of Lisas that tell you the manufacture date and plant in a document called "Good Things To Know About The Lisa.pdf" from SunRem, but not sure that a similar scheme applies to the mice. It does appear that the newer mice that came with the Mac 128 to the plus had a different serial number scheme than what's on the Lisa 1 mice. And to add more confusion, they all have the same model number.
I wouldn't go by the serial number as much as the shape.