It's possible, not sure what exactly is going on there with this version. From the image, I can tell this is MonitorOS and not LisaOS, so it wouldn't have the same machine monitor, though it may have a similar mechanism. Likely what I'm seeing here is a Monitor menu, which is set to auto start with the test application, but somehow there's a way to reach it and launch other programs off the disk too; so that's the interesting bit. (Monitor OS predates the Lisa and was more similar to the UCSD Pascal p-system VM, unlike Lisa OS/LPW, it doesn't make use of the MMU at all, and has a different file system.)
Since the mouse seeking behavior is totally off, it leads me to suspect it uses different memory variable addresses for the X,Y position of the mouse than other versions of LisaTest I've tested with, and even though LisaEm detects it properly as LisaTest, the mouse misbehaves. (Alternatively new bugs were introduced in 1.2.7 which broke COPS handling, but I don't recall messing with that code between 1.2.6 and 1.2.7 - then again this version does boot up and somewhat work in 1.2.6, so that is a bit odd.)
Most likely the COPS protocol went out of sync and mouse events being sent were interpreted as keystrokes, so one of them triggers this - I've also had other attempts to click on the test buttons cause LisaTest to shut down the Lisa, and in other sessions LisaEm telling me that the COPS queue is full - i.e. LisaTest stopped reading the event queue and the event queue is full.
I'm going through the IRQ 1 ISR disassembly to see if I can find out what the X,Y coordinates are in this version, and how to detect this vs other versions - if that's the actual issue.
Edit: I fired up 1.2.6 in a VM and verified that NMI does not enter this screen, I tried all the other keys and none work. Pressing any random key such as numerics or alphas makes the menu bar double in size temporarily and then go back to normal. The mouse does work properly, so it's unlikely that the X,Y locations in memory are different than in 1.2.7.
Looks like Shift-S (in raw keyboard mode, but no always repeatable) takes LisaTest out of "Consumer Mode" and produces a tech mode with an Options menu, but so far haven't yet found the key combo for the hidden Monitor screen. This is documented here:
http://bitsavers.org/pdf/apple/lisa/service/072-0085_Level_1_Lisa_Technical_Procedures_Mar85.pdf on PDF page 387.
Perhaps one of the PDFs on bitsavers under the Pascal Monitor directory has something... Looks like Monitor_12.0_Release_Notes_Apr83.pdf on p4-5 mentions a process manager, but doesn't say how to switch to it from a running app, likely this is what was invoked.