Ask Mr. Smarty Plants

Underground paving is a little out of our line, since the Lady Bird Johnson Wildflower Center specializes in the care and propagation of native plants. A couple questions you need to ask yourself before you make your decision are: How many square feet of lawn would you have to cover in topsoil to make it all level and the dirt over the slabs deeper? Do you grow annual grasses from seed, or do you have perennial grasses that grow by rhizomes and runners?

If you have perennial grasses that make a sod, throwing topsoil on top of that to make the depth equal with what you have to put over the slabs is just going to mean your grass roots will grow down to the sod, now underground, and probably will not prosper. If your grasses are annual, and die completely back in the winter, you could rake that, even leave the dead grasses as compost, and cover with several inches of topsoil. We say "several" because we don't know what grasses you grow or how deeply their roots are going to reach, and, therefore, we don't know how much height you need to add to the dirt over the slabs. Unless you intend to have little hillocks over the slabs, you are going to need to spread the same amount of topsoil over the entire lawn. 

Second possibility, you could pretend you planned it this way, and put raised, walled beds over the slabs, tilling up the grasses and removing them, hopefully before they seed. This website Raised Garden Beds (eartheasy) will help introduce you to the concept. You can then plant colorful flowers and quit worrying about the grass. This will require some expenditure of time and money, obtaining the materials, assembling the beds, and adding good soil and compost to the beds. 

Finally, you can do what you said you didn't want to do, and go in after those slabs. This would require some heavy equipment and hauling, and then you would still have to put more soil in there to make up for the concrete that has been removed. 

And, if you ever find out what those slabs are, let us know. We're dying of curiosity.