According to what I read that Pat Lansa wrote about her first Lasagna Garden she planted right after building that first bed. Build up that bed and move the strawberries.

Here is a link that might be useful: Lasagna Gardening 101

Strawberries do excellently under a thick layer of pine needles. I have left that layer on in the Spring and the berries will come up through about 3 inches of needles and be dirt-free for the season.
You may consider that to be your 1st layer... :)