Limestone Peak is not listed on LOJ, nor is it named on the topo maps.
I don't know whether the following is sufficient for it to be listed on LOJ , but it is listed on Peakbagger.com http://www.peakbagger.com/peak.aspx?pid=23437, and it is referred to in the Summitpost page for nearby Piute Mtn. http://www.summitpost.org/piute-mountain-white-mtns/155397 (see the additions and corrections section at the bottom of the page).
In addition, we found a large notebook register in an ammo box on the summit that showed a summit elevation of 12,277 feet. It was left on 7/20/04 and is quite full. The summit's in the Mt. Barcroft quad in Mono county. My GPS showed the summit coordinates to be 37.5300, 118.2097. Nice summit!