All my raised beds were made using cardboard on the grass.
That was 4 years ago that the first beds were made.
They're great. Only thing I can suggest is if you have any larger plants ready to go that you dig the holes for them first and lay the cardboard around them. It's easier than having to cut through the cardboard after you have put the top soil on.
Just make sure you wet the cardboard really well before adding the topsoil/compost/etc

I didn't have any problems with grass coming through.
Oh, and just be sure you use plain cardboard, none with the laminated plastic on the outside. The plastic won't break down.
The cardboard breaks down very fast, it doesn't take long before you have heaps of earthworms.
I prefer cardboard to newspaper but do use newspaper to patch small bits that don't fit.

No. I will leave it at that for fear of offending anyone. The only thing that has worked satifactorily is raised garden beds, which were filled with 2' of soil and I never had grass come through those.

I tried edging and Roundup for the first time last year and will never go back.

Mine have been great. I wouldn't do new beds any other way. I use newspapers as they are more readily available than cardboard. I think the first bed I did was probably 6 or 7 years ago.

Most of my beds are lasagne beds as well. I layer old leaves on the cardboard, soil, grass clippings, more leaves, more soil. With some beds, i've covered them in black plastic for a couple of months to hasten the breakdown of the leaves. The soil in these beds is just beautiful now.