Leizer is short for Eliezer, a Hebrew male name. Cerne is probably Czarna (pronounced Charna, with a ch like in charm), a woman's name, from the Polish word for "black." Breine or the diminutive Braindl or similar is a Yiddish name for women, meaning "brown." Polish and Yiddish names were quite common among Jews, especially women, and not everyone had a Hebrew name. As far as what their English equivalents might have been, people who anglicized their names often chose something that sounded similar to the original, or started with the first letter/s of the original, but not always.

All the best,
Miriam Bulwar David-Hay,
Raanana, Israel.