The New 52 version of Black Canary combines Dinah, the first, and Dinah Laurel, her daughter, into one story.
Black Canary has undergone a few origin stories in DC’s history, but the Arrow version most closely resembles that of Dinah Laurel Lance, the second one.
In fact, Dinah would also lose her husband, Larry Lance, leaving her to raise her daughter, Dinah Laurel Lance, by herself.
In the case of the second Black Canary, Dinah’s daughter, her childhood was spent surrounded by the heroes her mother worked alongside.