Both the roundup and lasagne method work really well but like the the others mentioned- it all depends on how fast you want to be planting.
I do the layering over the winter and the roundup in the growing season. If you use round up you can be planting in 15 days or so. I did use a small tiller- similar to a mantis tiller and that made working in the new organic matter so much faster.
Whatever you do you need to be able to put the time in to raking/ sifting/ picking out as much of the grass root as possible. Any little bit left in the bed can reannimate and grow. So we'll see how well I did when spring comes huh?

BTY roundup breaks down completely after about 5-7 days so I do use it in my IPM garden when i start a new bed.
Call me- Dolly