800K drives ... run their ejection mechanisms constantly
Apple changed the 800k drive version at some point, and this was the symptom if the newer version was put into one of the earlier Macs.
I think the version change may have corresponded to removal of the "auto-inject" feature of the earlier drives, where the earlier drives would sort of finish the insertion of a disk for you with a snap action, while the later version required that you keep pressing the disk in until it dropped down with a more manual feel like the 400k drives. (Or maybe I've got that backwards.)
The newer drives (or some at least) used a ribbon cable with a yellow stripe instead of a red one. Those cables are missing conductors in the 9th and 20th positions. That isn't evident unless you look at the end of the ribbon where you can see those are solid plastic whereas the others contain obvious metal strands.
So disabling the constant eject requires disconnecting one or both of those. (Perhaps someone else knows if both need to be cut?)
Since you probably don't want to modify your Lisa's cabling (so you can use a 400k drive in the future), you might purchase/make an extension or something similar.
eg. cut wires 9 & 20 of DigiKey part# H3AWH-3006G
edit: added some details, DigiKey part#, corrected some errors and made new ones