According to sources about Little Moreton Hall "The Moreton family's roots in Little Moreton can be traced to the marriage in 1216 of Lettice de Moreton to Sir Gralam de Lostock, who inherited land there; succeeding generations of the de Lostocks adopted the name of de Moreton.[8] Gralam de Lostock's grandson, Gralam de Moreton, acquired valuable land from his marriages to Alice de Lymme and then Margery de Kingsley. Another grandson, John de Moreton, married heiress Margaret de Macclesfield in 1329, adding further to the estate."
It seems clear that this is the Letice in question but according to this tree her descendants are not de Moretons or Moretons.
Perhaps one of these wives (of different fathers) is wrong
http://www.geni.com/merge/compare/6000000028359971836
If you have a source for descendant name change (which descendant) you could go ahead and make the notations within that / those profiles as the next step.
Tag Geoffrey Geoffrey de Lostock , Gralam II Gralam de Moreton , and John (who isn't in Burke) John Moreton .