Its good that you are building a lasagna garden. They are really best if left to overwinter, which is why most are built in the fall. Any time is better than no time tho. Rabbit manure is very low in Nitrogen (N) so it wont burn plant roots or cause too rapid growth. Chicken manure is very high in N, so either apply it in the fall to overwinter and season some or use it very sparingly. Horse manure is somewhat higher in N than cow manure and used to be used to bottom heat coldframes by layering it under the soil in the frame. As it composted, it generated heat that allowed for starting seeds early. Not so much needed nowadays, but possibly useful for the future.
I like Lasagna gardening cause its lazy. Nature doesn't dig and neither do I anymore. The Lasagna method emulates the way Nature builds soils and recycles nutrients. Because the bacteria that breakdown the layers are in the soil, and the manure is what feeds them so they can accomplish the breakdown, the manure should ideally be spread throughout the layers evenly. It isn't rocket science tho, so don't obsess over it.
Slightly off topic, but since you are Lasagna gardening, you might want to try planting spuds without digging as well. Mow the area, lay cardboard pieces in a row, set the eyes on the cardboard and cover with a foot or two of waste hay or straw. Water well and don't allow to dry out until the leaves poke thru the top of the hay. Keep the waste hay at a foot or two deep (as it decomposes, add more). The eyes will send roots down thru the cardboard and set spuds on top of it. For harvest, just pull the hay aside and pickup the spuds. For that matter, you can 'noodle' some young spuds about the time the greenbeans are ready (when the potatoes flower). The plants will just set some more tubers to replace the ones you harvest early. Don't use the hay on potatoes two years in a row. Spread it in the fall for next springs beans or corn. Enjoy
