Your question has compelled me to find out what the lasagna gardening method is. i have to say that I have tried something like it over the years - anything to avoid all that digging and turning over of the soil year after year. It would save the yearly turnover of 'new' weeds appearing and save your back!
It seems like a really good simple method of layering over the existent soil with composting materials and just building up the nutrients as you go.
These days I use the black plastic sheet method, which kills the grass and weeds underneath and leaves a nice 'clean' patch of soil to work on. I don't dig, just sow and plant directly into holes or furrows marked out with added compost. Then I layer up with more compost as a mulch.
I get the plastic 'free' from the skip of a local hardware store, who would otherwise be recycling it. It's best left on over winter.
I would think the layering of composting materials in the lasagna method would work well over the winter as well, so that the composting needed would be finished by Spring.