Hi Stephen,
I would do them in the same order Eric recommends. It would make sense (in my mind) that the nitrogen source being between the two carbons will encourage break-down, especially with the cardboard. Also (again, in my mind), it would seem like the
carbon would tie up, at least, some of the nitrogen, to help minimize it burning the plants.
The only thing I can think to add to what Eric said is to wet down the ground, cardboard & manure well prior to putting on the next layer.
As I prepare my beds for planting in the next week or so, I've noticed the rabbit manure & chips I laid down last fall are still fairly thick, so I'm hoping it will work to dig planting holes in the mulch, and filling the holes with pockets of soil to put the seeds/transplants in. That may be something you can consider doing if your lasagna hasn't fully broken down at planting time. You just may want to poke a hole in the cardboard when planting if it's still intact
enough to block the
roots from getting to the soil.
Good luck & let us know how it turns out!