If the depth of the soil in the raised bed will be 4 inches or more then a cover over the lawn that exists is not necessary. The only thing a covering would do is keep what is growing there now from getting access to the sun all plants need to grow and the depth of soil will do that quite well.

A good soil for growing much of anything is a mix that is about 45 percent sand, 25 percent silt, 25 percent clay and 5 percent organic matter. Do not accept what is euphemistically called "topsoil" or a soil mix containing 50 percent organic matter because more organic matter is not alw2ays a good thing.

If you have Bermuda grass, no weed barrier will work very well for very long. I would suggest digging it out and also removing all of the grass several inches out around the perimeter of the bed as well.

Other types of grass may not be as invasive.

I would never leave grass under a raised bed exposed to soil. Some grass species are very tenacious and will grow right through even a thick layer of soil. Layers of cardboard will stop most but some are best dug out entirely. Otherwise, you will be dealing with weedy grasses growing in your bed endlessly!

A standard 4'x8'x8" bed takes a lot more soil than you might think....almost a full cubic yard!! That's a LOT of bagged soil. It is far less expensive to purchase soil in bulk from a landscape supply or soil yard....by a factor of 3-4 times. Look for a landscape or garden planting mix, sometimes called a 3 way mix. Bagged soils seldom measure up to this very basic bulk soil product.

"I would never leave grass under a raised bed exposed to soil. Some grass species are very tenacious and will grow right through even a thick layer of soil. Layers of cardboard will stop most but some are best dug out entirely. "

I totally agree with gardengal.

My approach (for what it's worth) is not to fill the raised bed with soil I buy or haul in, but rather to remove the grass and then bring the level of the existing soil up by amending with compost and then tilling it in. The compost plus the air added in to the soil is usually enough to raise it four inches or so. Then, if you keep adding compost and mulch over the years the soil level will continue to come up another couple of inches.

The downside is that this is real work. You will want to work the organic material in at least six inches (in well drained soil) or may a foot or more if there is a lot of clay or drainage issues. That's a lot of digging. But, on the other hand, you only have to do this once as long as you never walk on that soil.

I did a lot of new raised beds last year on what was previously grass. I got the local nursery to dump a load of compost that I spend a week or so working in to the beds, turning them over several times. (If you are not up to the shoveling, find a couple of local high school boys that would appreciate some weekend employment.)

This year there are no spring chores to prepare the beds. They are under six inches of shredded leaves, which are keeping the weeds at bay. When it is time to plant, I will push the mulch aside and I am ready to go.

The advantage of this approach is that you are using all the minerals and critters that are already present in your soil - and just making it a better place for them to live, rather than cart in an unknown material that probably has issues of its own. You already have garden soil - just make it better.

I have a bluegrass, fescue mix lawn, and I used cardboard on the bottom of my raised beds, and my lasagna beds. Worms loved it and no grass survived. The best time to make a raised bed would have been fall. I put the cardboard down, add a couple inches of horse manure, chopped up pumpkins, fall leaves, and whatever compost I had laying around. By spring it's good to go.

Now, I would use an online calculator to figure out how many yards of soil you need, and call around and see what the cost would be. Make sure it is screened topsoil, not just fill.