Using the SteveMorse.org search option for checking the NYC marriage license indexes, for a person whose first name starts with Lil, and last name starts with Loeb, I found two possible entries. In 1945, a Lillian Loeb married a David Boyarsky in Manhattan. Also, in 1960 a Lilli Loeb married a Max M. Oppenheimer in Manhattan. There is no way to tell the birth year of either of these women, or if they were born in Germany, but looking into them or these two men further might yield some clues.
Lak/Lok/Liak/Lock and Kalon/Kolon in Zagare/Joniskis/Gruzdziai, Lithuania
Lak/Lok/Liak/Lock in Plunge/Telsiai in Lithuania
Trisinsky/Trushinsky/Sturisky and Leybman in Dotnuva, Lithuania
Olitsky in Alytus, Suwalki, Poland/Lithuania
Gutman/Goodman in Czestochowa, Poland
Lavine/Lev/Lew in Trenton, New Jersey and Lida/Vilna gub., Belarus