They recommend about 10 layers of newspapers for lasagna garden so It does have to be fairly thick for the best control. At least for me with all this Bermuda grass.
I like cardboard too if I'm putting mulch over top of it to keep it in place. Yesterday I used some of that gray foam that came as packing in a box. It's very light though so does have to be weighted down or pinned to the ground. Just experimenting to see.