Thanks for answering my question. Your idea about using the random LFO values to randomize various chosen parameters: that's a good idea, I will try that.
I also am using the software Max, with which I can send a burst of random values to selected CC#s on the Preen, more or less duplicating the action of Randomize menu.
Not sure what you try to do.
Triggering a new random value when one midi CC# change ?
No that's not possible.
You can use some CC (1, 2, 115, 116, 117, 118) to control a matrix multiplier where the source is a LFO with a random shape.
I think that would be the closer solution.