Is there anything I can do? I have read that raising the surrounding yard will disrupt its drainage and maybe kill it. Why don't the live oaks in Austin and Hill Country seem to have this problem?
Live oak elevating and destroying my sidewalk really bad!
Texas has two species of live oak. Austin and the Hill country west have Quercus fusiformis. It could be that this species' roots are not as shallow. You are correct. Elevation changes as little as 1" - 2" will kill an oak tree. Removing the elevated sections of your sidewalk and scraping off dirt and roots to bring the level down is the only thing I can think to recommend. You will do some root damage, but your tree should recover. Although it is not always possible, if you can, reroute the sidewalk.
http://www.efloras.org/florataxon.aspx?flora_id=1&taxon_id=233501031
http://aggie-horticulture.tamu.edu/ornamentals/natives/quercusfusiformis.htm
http://www.sbs.utexas.edu/mbierner/bio406d/images/pics/fag/quercus_fusiformis.htm
http://aggie-horticulture.tamu.edu/ornamentals/natives/quercusvirginiana.htm
Maybe you could remove the old sidewalk and build a new sidewalk out of wood, so the tree can breath.