Well, after Lisa2's reassurances on the Datapower PSU, I have reassembled and powered up the Lisa.
Good news, there is life in it!
I get beeps

The bad news, trouble with the monitor part, totally does not come to life.
Just stays pitch black, no lines, small dot, nothing.
I'm still pretty optimistic, as long as the actual tube is not dead we still stand a chance.
Computerwise I do think it looks rather good, with the drivecage installed the the widget drive spins up (noisy bugger that is), stil get the beeps (three beeps, well, actually rather loud, one second, beeps, evenly intervalled). I don't hear the brake release, but that's problems for later...
So, any tips on how to attack the monitor part? I assume there is an analog board in there, pretty much like the compacts, it's the only part I have not yet seen as it seems to be pretty well hidden in there.
Totally dead tube to me usually meens bad/cracked soldering on the analg board, totally dead flyback transformer or possibly PSU issues.