Yes, they'd be in a hole.

A better solution would be to strip out the sod, amend the soil in the planting holes when you plant perennials, and mulch over everthing.

Be careful stripping the sod close to the existing shrubs. Some shrubs, like Azalea, have very shallow root systems.

All that Lasagna Gardening really is is composting in place. Whether your shrubs would be in a "hole" while the material you put around them is digested would depend on how thick you made that pile of material. I would not suggest a Lasagna layer a foot thick but a few inches will do good things and little harm.
There is no real good reason to dig out the grass that does exist there and starting with a layer of newspaper is all that is needed, mostly, to eliminate most grasses. If the grass that is there is one of the invasive species (Quack Grass) digging that out and putting in a good barrier before going further will cut down maintenance later.

Wouldn't you also smother the roots of the shrubs as you smothered the grass?

I hadn't thought about smothering the shrubs' roots. I'm definitely not pulling up the sod. I've done several lasagna beds with excellent results. Maybe I could carefully kill the grass in a ring around the shrubs and just put mulch there and do the more traditional lasagna farther out with the newspaper, etc.

The reason newspaper will smother the grass is because the grass needs light to grow. shrubs will have their growth above the newspaper so it should be ok to use under the shrubs. However do not use a really thick layer of layers under the shrubs, keep it away from the trunks because it will end up rotting out the trunks of the shrubs.
Sandy

I did that last fall over an existing mixed planting bed. There was no grass there to kill off, but I used newspaper to kill off a few weeds and prevent reseeding of flowers that I didn't want to come back. I layered mostly leaves and grass clippings, a little other yard waste, coffee grounds, etc., keeping the stuff a few inches away from the plants. I only used about 8 inches total. In spring that old worn out soil was beautiful loamy black soil, only slightly higher that what I started with, and the plants weren't in holes.

This fall I did something similar to a different bed with poor soil. I didn't use paper as there was nothing to kill off. I basically just mulched the whole bed with grass clippings and leaves about 8 inches thick, so it's not really a lasagna. I did it around the first of Oct. and a few weeks ago I couldn't stand the suspense so I had to take a trowel and dig down to peek and see what was happening. It's looking good and teeming with big fat earthworms. This was built up around small young shrubs like boxwood, leptodermis, japanese maple.

So if you limit the depth of your materials and don't pack the stuff next to existing plants it works great.

Karen

Heavens, why would you want to take so much time to give to your shrubs the care they deserve. Strip away the sod...it shouldn't be there in the first place. Lasagna gardening has a place....but not in the vicinity of shrubs and trees.
A little grass removal is called for, then improve the soil for the shrubs ongoing health.

I have a large bed that runs across the whole front of my house. There is a large Hibiscus, Cape Honeysuckle, and a ficus bush (was a tree but its been cut down so many times). Under all this I had a mess of Ruellia that grew like weeds. I finally pulled as much of the ruellia out that I could get and then I lined the whole area with cardboard, then bagged manure, grass clippings, leaves and covered the whole mess with wood chips. None of this has hurt my hibiscus, honeysuckle, or ficus. The soil is definitely a lot better as I now have some earthworms in there that weren't there before. It's not totally decomposed yet but I know that what I do plant in there next will be far better off. Go ahead and give it a try. Won't hurt your shrubs a bit.

Pam

Stripping away sod, or digging out grass growing where it is not wanted is more time consuming then is placing newspaper and covering that with a mulch, and it is much more work.

Plus by leaving the sod there, wont that give the soil nitrogen as it breaks down? OR does it have to be taken up and turned over in the bed to give it nitrogen? I think removing the sod would be uncalled for. If you're like me, one step less is much less work because I am tending to lots of acreage here.

I have two butterfly bushes book ended by two rose bushes all in a single row. This spring I built a 10 inch deep lasagna bed around all four using cardboard on the bottom followed by layers of shredded oak leaves grass clippings peat some cow manure and topped with bark mulch. All four plants were transplanted to their current location before the bed was built. So far so good but I too have a concern that the buried plants are too deep, just have to wait and see.

No worries Rich- they'll be in 4" or less compost by the end of the summer

I don't know where in IL you are, but I'm in Rockford. I've used the lasagna method around established roses, trees and shrubs many, many times. It will actually benefit your shrubs because it will keep the soil around their roots moist and it will eliminate the competition from grass and weeds around their roots. There will be no negative effects except sometimes small areas of newspaper become exposed and even tear away and have to be removed or recovered with organics. Not a big deal.

Put down newspaper (I recommend 10 layers) to within 6 inches of the shrub trunks. Layer over the newspaper with 6-8 inches of fresh organic matter or 4-5 inches of compost. The shrubs will look like they are in a basin for a while. Within a few months 8 inches will have compressed to 2 or 3 inches. By the following spring the area will not be much higher than the sod around it. At that time you can cut your edge into the sod and decide what you want for permanent mulch. 10 layers of newspaper and organic matter will absolutely not smother the roots of your shrubs. In fact, digging around trying to remove sod will do MUCH, MUCH more damage to the shrub roots. Good luck with your project.