Maybe an organization M----- W----- F------? M-Something Women's Federation? I seriously doubt that it's a personal monogram, although the LM might be, I suppose. Definitely organizational.
sometimes things just present themselves........... http://www.ebay.ie/itm/VINTAGE-West...hash=item25d9ab2699:m:mx8dP4onJU6ziYTZOgJZuZw
Women's Missionary Federation - Life Member? A possibility, but I wasn't able to find anything to match it.
Usually this style of pin is academic related. I have seen a couple which were travel souvenirs. They are usually Mid '20s to mid '40s. The deconess looks '30s to me.