Check the 5 V setting pot (R29, 500R) on the power supply board. If the slider loses contact with the cermet track, the output voltages will increase until they trip the crowbar thyristor. This can happen once after warming up (power supply simply switches off) or frequently (power supply makes clicking noises).
As mentioned above, the golden RIFA capacitors usually need to be replaced. Use X2 resp Y2 parts to comply with your local safety regulations. The power supply also works without these parts, but EMI will be above CE resp. FCC limits.
Of course, electrolytic capacitors can fail after some time, just like any other component. But with THT electrolytes from the 80s there is definitely no need to replace them prematurely. The quality of these parts is much better than "consumer grade" components you can buy today. If something needs to be replaced after all, use components from well-known manufacturers (like Nichicon, Panasonic, Nippon Chemicon, Elna...), buy them from a reliable dealer who can give the exact type designation (no Chinese mail order!), and check the specifications in the manufacturer's data sheet. In this way you will achieve a service life of about 10 - 20 years again.
(SMD electrolytic capacitors from the '90s are a different issue. Some series, like the ones used in the Mac II family, in Tektronix testgear or Sony Hifi equipment, tend to spill and must be replaced now!)
Elcaps from the '80s and before lose their dielectric oxide during storage. This results in an increased leakage current, but can be cured by running it at its rated voltage for some time. Parts from the '90s and later have oxidizing electrolytes. They do not degrade during storage, but if they leak damage to the PCB tracks will occur.
To force the power supply on, connect the ON signal to +5Vstby. On the PSU connector ON is pin X and +5Vstby is pin 20. For standalone operation you will need some load at +5 V and +12 V, an automotive headlight bulb works fine for the 5 V rail, and a 5 W lamp is sufficient for the 12 volts. To build a test rig, get a "JAMMA Arcade" board edge connector from ebay and cut it to the required length.
To force power-on from the Lisa I/O board, bend U9F pin 24 out of its socket (or remove the COPS421 completely) and connect U7F pin 11 to the standby voltage (U9F pin 9).
One electrolytic capacitor that frequently fails is C8 on the CPU board. If it has an increased leakage current, the reset generator hangs and with it your Lisa, she shows a random pattern on the screen. The capacitor can be replaced or, if you want to leave the board in its original state, it can be regenerated by connecting it to its rated voltage for a few hours with a 10k current limiting resistor.
