I use the no dig for potatoes Northener. The first year we made raised beds directly on the lawn. We covered the lawn bits in the beds with thick cardboard - soaked the card, then topped off with 8" to 10" of well rotted manure.
When I planted the potatoes (only a week or so later) I just moved the mulch to one side of where I was planting, cut a cross in the cardboard. Took the grass off the planting hole, dug a hole about 3" deep. Spud in, cover with soil, pull cardboard over and pull mulch back onto the cardboard.
Its an individual preference, I found the above method much more labour saving as I didnt have to keep earthing up with manure. Just throw some grass clippings on to help with moisture conservation and assist in reducing light levels.
It all depends what weeds you are trying to get rid of, perennials need to be dug out even in a no dig system. But you can quite happily cover annuals and lawn grass which will not survive this method of gardening. :D