1. When I turn on the machine, the light under the screen turns on and the screen is dark for a while, and after a while a grey screen with a pattern of diagonal lines shows up on the screen;

Replace capacitor C8 on the CPU board (2,2µF next to the 68000). It gets leaky, then the 555 is not able to finish its /Reset pulse.
 
2. I don't have a keyboard for this Lisa, but I've read that it used a TRS style connector. Is there, to anyone's knowledge, a converter for keyboard signals, either from:

This has to be invented first. A direct connection is not possible, you will need a protocol converter that would accept USB, PS/2 or ADB and generate Lisa Kbd signals.
 
3. This computer didn't come with a floppy drive inside. Can I install a 400k drive from a Mac 128k or a 128k external drive?

Yes, it is the same drive.

I also noticed that there are 2 floppy drive ribbon cables inside the floppy drive cavity - is this normal?

Yes, that's normal. A Lisa 1 has two 26pin cables for its two Twiggy drives. A 2/5 uses one of them to connect a Sony 400k drive (via a PWM generator board for the variable motor speed). A 2/10 also has two cables, but there one is for the floppy (20pin), the other is for the hard disk (26pin).


Regards
Patrick

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