No, it has nothing to do the Italian pasta dish.
"Lasagna gardening" is a method of building rich soil.
It was one of the very first ways I learned to grow food when I started organic gardening 7 years ago.
My mentor and dear friend was a German horticulturalist named Marielu. She implemented what German's call Hugelkultur raised beds all over her self-sufficient homestead, and let me tell you: the place was THRIVING.
Starting with compacted hard clay
But our new garden was rock-hard clay, basically concrete.
I asked Marielu how we would ever have a garden like hers if our soil was so terribly compacted.
She grinned: "I started with the same exact clay that you have".
The Hochbeet or Hugelkultur (German for "raised/mound bed") method is a practical way to create a self-fertilizing, composting raised bed. It has been used for centuries all over Europe.
The process is simple: pile different organic matter on top of each other to create a raised garden bed with zero tillage or digging.
This is also sometimes called a "lasagna" garden or "sheet composting" because of the layering.