Not true.
Carpatho-Rusyns from Slovakia (like my paternal grandparents) never use the term "Lemko" to refer to themselves. They use it to refer to Carpatho Rusyns across the border in Poland (i.e. my maternal grandparents).
It's really just semantic, they are ethnically nearly identical, but the terminology was not.
Lots of interests wanted to confuse the identity of these millions of immigrants of the early 1900's.
However, your grandparents culture was very Lemko/Ukrainian right down to the Easter and Christmas traditions - easter eggs, babka, horseradish and beets, caroling.
Can you imagine how the political landscape would change were the Irish talked into forgetting their identity?
"Carpatho-Rusyns from Slovakia (like my paternal grandparents) never use the term "Lemko" to refer to themselves."
Actually, Lemkos at one time settled well south of slovakia into Yugoslavia and Bulgaria.
http://64.233.161.104/search?q=cache:etAhX-jTCTUJ:www.encyclopediaofukraine.com/pages/L/E/Lemkoregion.htm+lemko+villages++in+slovakia&hl=en&ie=UTF-8