The lullaby I use most regularly with Helen is the song "Donna, Donna, Donna, Donna", one of the few songs I remember from my own childhood. I remembered the lyrics surprisingly well when I started singing it to Helen, so I think my mother may have sung it to me as a lullaby too.
The interpretation of the song is debated: is it a metaphor for Jews in the Holocaust, perhaps "a political statement in Israel during WWII to encourage resistance vs. Nazi racism", or a mystical parable? My guess is that the song is a Diaspora expression of relief at having left Eastern Europe, along with a general fear for those left behind: a Yiddish performance in New York seems unlikely to have been Zionist, while the Holocaust per se only started to become known in the US in late 1941.
Courtesy of YouTube, I discover that this song is popular in Vietnam, there is not only a Vietnamese version, but a French one (directly translated from the Yiddish). And there's a version by an Indonesian singer. And of course a Yiddish version.