I have found some old pictures on a WW2 memorial where, under the pictures of two women showed a rank of LA.W. and L.W. respectively. A quick Google search didn't help so I thought this would be the place to ask.
I wonder if LA.W was in any way related to "Leading Aircraft Woman", which was the E-3 equivalent in the RCAF Women's Division. But, Canadian ranks are not my specialty, and this is a guess, based on lists of actual ranks. I can't find anything which could translate to L.W, so I still wonder if this is some kind of duty description rather than rank.
It might be helpful if you could at least identify the service-- i.e. were these ladies Army, AF, Navy, or Marines? Were they in uniform? Did their photos on the memorial give any indications? A photo of their portion of the memorial might help us give you some answers. I suspect that we are looking for job titles rather than ranks, as I have never heard of such abbreviations for rank. Are we assuming they were US?