If the ancestor born in 1893 in New Jersey was 100% Jewish, then this person would have had both a Jewish father and Jewish mother, and not an Irish mother.
From looking online, the earliest known home for unwed Jewish mothers opened on Staten Island in 1910, so long after this ancestor was born. It is possible that this ancestor was given to the Foundling Hospital in New York City, where they took in newborn babies, regardless of ethnic background. That might explain how a baby who was partly (or 100%) Jewish ended up being adopted by an Irish family.
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Michele Lock
Lak/Lok/Liak/Lock and Kalon/Kolon in Zagare/Joniskis/Gruzdziai, Lithuania
Lak/Lok/Liak/Lock in Plunge/Telsiai in Lithuania
Rabinowitz in Papile, Lithuania and Riga, Latvia
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