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.
Yep here it is, Technical Introduction to the Macintosh Family p. 227:
”Note: On the older 400K disk drives, a buffer in RAM (actually the low-order bytes of words in the sound buffer) is read by the Analog Signal Generator (ASG) to generate a pulse-width modulated signal, like the sound signal, that controls the speed of the disk motor. This speed variation is responsible for the characteristic humming of the disk drive. The Macintosh Operating System uses this speed control to store more sectors of information in the tracks closer to the edge of the disk by running the disk motor at slower speeds. On the BOOK drives, the variable disk speed is automatically controlled by the disk drive hardware.”
You need to recap it before you do ANYTHING with it period.
These logic boards are known for failing catastrophically with bad caps. Sometimes to the point where you end up the waiting queue for a replacement logic board as a few others are in.