The oldest synagogue in NY is Congregation Shearith Israel. It is a Sephardic congregation. The Lazarus family was a prominent member of the congregation. The congregation has several cemeteries - it might be possible that a member of the family is buried in one.
The congregation is still operating. https://shearithisrael.org
There may also be some records at the Center for Jewish History https://www.cjh.org/
Secaucus NJ USA
HASSMAN, SONENTHAL, DAUERMAN, LUCHS - Drohobycz, Ukraine
HIRSCHHORN, GOLDSTEIN, BUCHWALD - Dolyna, Ukraine
ELLMAN, COIRA, MAIDMAN - Minkovtsy, Ukraine
KAGLE, FASS - Ulanow, Poland