Sorry to hear your experience has been so negative Kirpi.
I used lasagne gardening for the first time when I took over my plot two years ago with great effect. It was, quite honestly, the best method I have ever used to set up a veg garden. Other plotholders still ask me what I do to my plot to keep my plants so healthy and vigorous.
I did find I had to compact each layer well as you built it up to stop air pockets and also not use too thick layers of one particular material. I also used HM compost mixed with shop bought (and did use peat based so not very P.C). We grew squashes, cabbages, strawberries, beetroots, salad crops, chard, celeriac and spring onions in these beds in the first season. Once established, I don't water my crops unless it is a real drought.
We used this method out of necessity at the time as we took over the plot during a very dry June and simply couldn't get a fork into the hard baked clay. In addition, the majority of my plot hadn't been cultivated in living memory and I don't like using rotavators and strimmers as I know the site is full of newts and slow worms.
The beds we built in this manner are still the most productive (they have been top dressed after each harvest with a little manure). They are currently filled with onions, shallots, chard, salads and garlic and doing really well - in fact I am hoping we will avoid the dreaded white rot which the other non-lasagne bed suffers from.
I am slowly surrounding the beds with edging and top dress them now using the no dig approach. However it was a great way to start off the plot
So much so that I am (hopefully) just about to take over a quarter plot and plan to do exactly the same as I can no longer double dig due to back problems and have been so pleased with the result on the other plot.
Perhaps it was beginners' luck but I am really surprised to hear your negative experience.
By the way, I planted squash, strawberries, beetroot and cabbages straight into the lasagne beds (which were topped with compost mix and weed suppressant because I didn't believe the couch grass and bindweed wouldn't get through the layers). I did get a little weed growth around the edges but nothing other than very weakened bindweed elsewhere.