Don't remove the sod. The rhododendron's roots are within 1" to 3" of the surface. Disturbing the soil can be fatal to the rhody.

Don't add any more soil or compost. Since rhododendrons are so shallow rooted, they are easily smothered. You can add 1" to 2" of mulch. I personally would spray with roundup before adding the mulch. I know a lot of people will cringe, but I am spraying weeds under rhododendrons with roundup all the time. It enters the green tissue that is sprayed and then kills the roots of the plants whose green tissue was sprayed. Of course you must take precautions to avoid any drift or spray getting on the rhody.

Here is a link that might be useful: How to care for rhododendrons

Tricia, do as rhodyman says. It works.
Did it in a large bed, approximately 4500sf and it works like a charm. The thicker the layer of mulch the better it works. If you'll do 3-4", round-up could be eliminated all together.

I'm confused. Are you saying I should use Round-Up to kill off the turfgrass in, say, a 10' circle around the rhoddy & then proceed to lasagne over the remaining turfgrass that's now in the area that will become our shrub border? Then, around the rhoddy...only place 2" of mulch after the Round-Up has killed off the grass?

We've got plenty of room to work with so we can gradually taper down the lasagne layers so as not to create a shallow/sunken area around the rhoddy. Right now, the rhoddy pops up in the middle of the grass area. We'd like to create a border approximately 12' deep and about 40' long with the rhoddy anchoring one end.

I'd never considered using Round-Up...glad I came here to discuss this before proceeding. I've never used Round-Up for anything more than just a quick hit on, maybe, something like an errant violet that refused to die from a crack in the driveway...guess I should toss a plastic tarp over the rhoddy before spraying just for precaution sake?

Also, about that black plastic edging that surrounds the rhoddy....is it okay to remove it? It looks nasty but it's clear from looking at it that the rhoddy's roots are raised up above the grass area several inches inside the plastic ring. Should we just leave things well enough alone & leave he ring?

Lasagna gardening is meant to be used when preparing a new bed. You apparently are referring to applying a mulch that the roots will grow up into. For rhododendrons that is not a good idea. The purpose of the mulch is to conserve moisture and keep the roots cool in the summer and insulated in the winter. If the roots grow up into the mulch, then it does neither. If the mulch is too deep it will kill the plant. Another worry, peat moss is not a mulch, it is a soil amendment. So I don't think that it is wise to try to think of lasagna gardening around an established rhododendron.

You only have to worry about the rhododendron roots out about to the drip line of the plant. So if you want to remove the sod or whatever, all options are open. It is just the area inside the drip line of the rhododendrons where you should not disturb the shallow roots.

I foresee another problem. If you build up the area outside the rhododendron drip line, the area around the rhododendron becomes a depression and water will puddle there. That is very bad. Rhododendrons should be mounded up from the surrounding soil. So I would say that removing the sod outside the rhododendron's drip line is much better than doing a lasagna or something that builds up the surrounding soil.

If you apply over 2" of mulch, the mulch starts to be a problem. It is recommend to only use about 1" to 2" of mulch. Mulch is there to hold in the moisture and keep the roots cool in the summer and insulated in the winter. If you use more, it can smother the roots or as mentioned previously stimulate the roots to grow into the mulch. A heavy deep mulch prevents the aeration of surface soil / roots and death quickly follows.

I think a large piece of plastic could be disastrous. If the sun hits it, the plant is literally toast. When you are done, it is big and awkward and contaminated.

When I spray near a rhododendron, I carry a piece of cardboard. I place the cardboard between where I am spraying and the rhododendron. I must mark which side of the cardboard might have roundup on it, or I could be making the problem worse. If roundup does touch a rhododendron leaf, either wash off the leaf with clean water or remove the leaf.

When using roundup, never use it on a windy day. Use a course mist that won't be affected much by any wind currents. Use a low pressure in the sprayer. A higher pressure tends to atomize the spray more. It is easier to get a course spray with a low pressure.

Don't use the new "Roundup Extended" around a rhododendron. It has a second chemical that is designed to provide residual weed killing for use around sidewalks and driveways, but not to be used in gardens.

Thanks...we'll go with removing the sod in the new border area rather than lasagne...& no tarp!

All this presupposes that it eventually stops raining & that possibility is not at all certain for the moment!