I bet there's an organic garden club near you, & they'll know about the timing on lasagna gardening in your area.

You might also post on gardenweb's Texas Forum.
There're lots of helpful & knowledgeable people "over there".

Best luck!

I've used lasagna gardening for 10 years. You can plant immediately. I use whatever I have. Two years ago I made a 40' x 20' bed. Cardboard as a base, peat moss, partially decomposed compost, freshly fallen leaves, fresh grass clippings, composted cow manure and a thin layer of bagged compost on top. The depth was about 18 inches. (clay underneath) Planted immediately and the plants thrived. The next summer, I hardly had to water and the plants loved it. You can use whatever material on hand in whatever proportions. I did use bark mulch on top to keep the weeding at a minimum.
Debbie zone 7 at the time