Just to check first: are you connecting the +5V sense line (connector pin N) to +5V? If not, the PSU might be thinking that it's undervoltage, and so it's pushing more and more power into the transformer to try and turn +0V into +5V.
The rest of this post assumes that you are doing this.
Yeesh, assuming your loads are set up correctly (looks nice btw! much tidier than mine), that's a spicy PSU, going overvoltage by 60%. I think it's fair to say that it's not regulating, but what is also interesting is that it isn't shutting itself down owing to the overvoltage (
Hardware manual PDF page 272, crowbar circuit mentioned at bottom). I would expect that +18V on the +12V rail would be enough to trigger the shutdown mechanism and, since that's not happening, would at least suspect something fishy might be going on with CR9, CR10, or its neighbours in the circuit.
To be clear, this problem isn't what's causing the overvoltage in the first place: it's a secondary problem in that the PSU does not seem to be ready to shut itself down if an overvoltage condition is present.
While I'm stalling for time, we can answer some other questions that aren't really relevant. +5V standby is actually a completely separate power supply within the power supply housing. It's a simple linear supply, and it's not too surprising that it works. (PDF page 273, "The Standby Supply".) Similarly, -5V is working because it uses a simple linear DC-DC voltage converter that changes whatever's on the -12V rail to -5V. Owing to the nature of how linear voltage converters work, it's going to be working harder to convert -18V to -5V than it would to convert -12V to -5V (and would get much hotter in the process), but your PSU is probably not staying on long enough for this to matter.
I'm afraid my own PSU repair skills are somewhat limited too --- there's a chance someone might jump in with some better ideas. It's fair to say that the Lisa PSU is not made in the way that more modern PSUs are, not that this would help me too much. Therefore, as we ponder and await an expert, why don't we collect what information we have first?
- Using the old Mark One Eyeball: take a very good look at the components on the board. Aside from the bulging caps, does anything look unwell? Are there parts of the board that seem to look scorched? Anything that seems cracked or fatigued? Solder joints seem ok?
- When you were running the PSU: did you notice anything that might be a clue? Stuff getting hot? Buzzing sounds? (Many Lisa 1.2A PSUs do buzz, so that might not be so unusual.) Smoke? Odours?
- As a kind of hail mary: what's going on with R29, the voltage adjustment trimmer? (PDF page 269, also
schematic bottom right) Maybe it's just preposterously out of trim --- is it set all the way to the stop in one direction or the other?
Another recommendation is: hit the books. Have a read of Chapter 10 of the hardware manual, which narrates how it works. Don't worry if you can't understand everything (I don't either!) --- although maybe your TV repair experience will help. Form some theories about things that might be going wrong, theories that sound like "maybe if this component is always on, then the primary side will keep pumping energy into the transformer". These components may be dangerous to check in circuit without special equipment (DON'T just plug in an ordinary oscilloscope and start looking for the waveforms on PDF page 268!), but one thing I could do is take some power-off measurements of those suspicious components in my own working spare 1.2A PSU, and we could compare if we're seeing the same things.
Finally, you might consider starting a conversation over on
lisalist2, where there really are some talented people who might be able to come up with an answer more promptly.
Unfortunately, you are correct to be concerned that the excessive voltages might cause trouble. -12V is probably not used for much that you have to worry about; -5V is fine; +33V is your screen which you said was at least coping briefly. +12V and +5V are likely giving all your logic a hot time. Hopefully it was brief enough that no substantial damage has been done.