Any idea as to where your Lithuanian line might have lived in Lithuania.
The LUNAS surname ending would likely have been spelled LIUNAS with the I being dropped in the U.S. to simplify spellings.
Depending upon the language used, Kaunas can be spelled multiple ways to include Kauen (German)/Kovno (Russian) or Kowno (Polish).
My mother's side of the family came from the Virbalis area of Lithuania and I have visited there back in 2008.
Tom S.