Question
Ronald-  I live in North Texas where the soil is notoriously thin and rocky. The 20 year old Bradford Pear that is in my front lawn (the lawn is 300 sq.ft. and is a Bermuda/blue/rye mix) has runners and major roots all over - leading to the lawn dying out (especially on the Southwest side). Whether seed or sod, there seems to be no way to get enough soil turned up and leveled out to make the contact with the ground the new grass would need.  I was thinking that I could spread 1" to 2" new topsoil and then plant the replacement. My only concern with that is killing the tree through depriving it of root oxygen uptake.
Your thoughts?  The spouse will simply no accept tree removal. Thanks.

Answer
Regrettably, I cannot offer a sustainable plan for a grass cover under the tree. I suggest that you explore ground covers. Contact  the Extension Office in your County for a durable species that will meet your conditions. I have seen Wedelia trilobata treated like a lawn and the appearance was quite pleasing.
My final (and over-ridng) thought is that we are only as happy as our spouses.