Faulty patch: it is always good to 'Load' a patch to run it from RAM before you store it, to make sure it works.
It is probably trying to load a faulty patch as the default.
Select a patch that works correctly, then press and hold down the encoder a few seconds, until the patch number disappears and appears again. This makes the selected patch the default next time you start up.
Sounds like your power supply does not support the inrush current required by your modules when you switch the system on. It is not an unusual problem in Eurorack. When power is first switched on, current flows in to charge those nice, big decoupling capacitors that every module has to smooth out power supply noise. If this happens too slowly due to limited current, then the voltage will rise slowly up to 12V and some modules might suffer 'brown-out' problems.
I would guess that your Lich will at a certain moment receive enough voltage to power on, but then it starts drawing current which contributes to pull the voltage back down below the regulator requirements. In other words, it doesn't start up cleanly. When you switch it off and on again there's still enough charge in the decoupling capacitors everywhere in your system that they don't pull the voltage down, and the Lich can get a clean start.
Sorry, that's a long explanation! tl;dr: If you want to get rid of this problem then make sure your PSU is strong enough.
