My great-great-grandmother was born Pessl Fallek in the town of Mielec in Galitziya around 1840. (I don't have a reliable source for her date of birth.) According to her death certificate, her father's name was Leo; according to her gravestone, it was Yehuda. In Nov. 1875, she gave birth to a son (my great-grandfather); his name was Leo in English, Leib in Yiddish, Juda on his marriage certificate, Leibish on his gravestone. Pessl came to New York in 1896 with Leo and died in Brooklyn in 1923.
There was a man named Eliasz David Fallek born in the town of Mielec. According to his death certificate [no image], he was born 1 Sep 1836 and his father's name began with an L (the rest, according to the researcher who found it but was unable to make a copy, was illegible) and his mother was Sara Cohen. According to records in JRI-Poland, he lived in Mielec and had several children. Several New York records give his occupation as Rabbi; he came to New York around 1902 and died in the Bronx in 1922. His gravestone [available at JewishData.org for those with a membership there] gives his father's name as "Aryeh Leib."
Pessl married Moshe Yitzchak Werdesheim. Eliasz's daughter Blime married Isaac Werdesheim. I do not yet have documention about how these two Werdesheims were releated, but the odds are very high (from other sources) that they were either uncle and nephew or first cousins once removed.
I really want Pessl and Eliasz to have been siblings. If it weren't for their gravestones, I'd have a moderately strong case. The question is whether the inconsistency in the fathers' names is significant. It's quite possible that in both cases the father was known to the later generation only as "Leibish". Note that the death certificates are consistent. But when it came time for the matzevah, perhaps the children wanted something more formal -- and since "Leib" is the second half of two common Hebrew/Yiddish name pairs -- Aryeh Leib and Yehuda Leib -- perhaps they each chose based only on "Leibish"... and chose inconsistently.
But in the back of my mind, I hear Israel Pickholtz's admonition: "If it might be wrong, it doesn't belong." If I'm honest with myself, this is just wishful thinking on my part. I need something more definitive to link these two together.