I should have checked with our applications engineers first, Lhmr is a new modified rating life calculation based on ISO 281:2007 that takes into account the stresses on the bearing components as well as lubricant conditions. This supercedes Lhna which was based on ISO 281:1990. The main difference between the two is the new rating is a more accurate estimation of the actual operating conditions then the older standard. You should be seeing this designation more often in the future.
Something you may not be aware of, the Lhmr or Lhna rating can be higher then the L10 life. The L10 life only takes into account the load on the bearing and the new life calculations can have a correction factor greater then 1 if the lubrication is very clean and there is a sufficient film thickness between the rolling elements and races. As an example, if the bearings are lubricated by a filtered oil system, the oil quality will be higher then for a sump and lead to longer life due to the level of contamination buildup in the sump system.