My recommendations are not for lasagna gardening, whatever that is.
IF there are lots of weeds to kill, a layer of thick cardboard is useful in the first season to keep light off them while they die, and plants can be set into the compost above while the weeds are expiring below.
From year two onwards, as long as you the gardener are conscientious about removing any weeds that germinate (an easy job), all you need to apply is a thin layer of decent compost to maintain soil fertility. In damp areas this is better than mulches such as those you mention, which tend to accumulate slugs.