I uploaded a similar post implicating that Dinah Drake could be the time displaced mother of Laurel and Sara but given her interactions with Quentin I've given up on this idea, as surely Quentin would point out that Dinah looks exactly like his ex-wife in her late-20s/early-30s. That said when Quentin meets Dinah he does look at her like he recognizes her and I still find it strange that her name is Dinah Drake, who traditionally is the mother of Dinah Laurel Lance and the first Black Canary. She is also a prominant member of the Justice Society of America. Also in the series Laurel and Sara's mother is also named Dinah whose last name is unknown, though I am certain I red somewhere that her full name is Dinah Drake-Lance. Coincidence maybe or perhaps simple oversight, but when is anything in the Arrowverse, a universe of shows with time travel, multiverse and magic is anything simply coincidence? I think, and it would be awesome if I was right, that Dinah Drake could be Laurel and Sara's grandmother.
This show does often change around family relations between well known characters such as Iris West and Wally West being siblings in The Flash whereas in the comics they are aunt and nephew, so Dinah Drake being Laurel Lance's grandmother would kinda make sense. I also think Dinah actually does have a slight resemblence to Laurel and she is quite like her. The car scene between her and Oliver in 5x12, the advise she was giving him, was definitely something Laurel would have told him. I think that she does also resemble Laurel and Sara's mother as I have always thought there was a good likeness between Dinah Lance and Laurel. Also Dinah Drake's choice of weapon is a bo-staff like Sara. I think it would be the ultimate justice if Laurel's successor, at least for the time being, was her own grandmother succeeding her granddaughter's mantle. That said Dinah would at some point have to travel back to some point in the past, the 1940s/1950s to meet someone and have a daughter also named Dinah Drake, Laurel and Sara's mother, to ensure Laurel and Sara's existence doesn't cease. Below is how I think it should be done.
I think Dinah should join the Legends in the third season of Legends of Tomorrow to substitute for Amaya Jiwe, as I assume she'll be leaving at the end of the season so her granddaughter Mari McCabe doesn't cease to exist, and she befriends Sara but later discovers their relation. Maybe Sara meets her grandfather, Dinah Lance's father, on a mission in the 60s but discovers that he isn't married and doesn't have kids as he should then they connect the dots. At first Dinah probably wouldn't except this but then Sara would begin to feel the effects of being erased from the timeline, similar to what happened to Cisco in The Flash 2x11 because of Barry's disruption of the timeline in keeping Eobard Thawne imprisoned in the pipeline.
With this revelation Dinah, unwilling to let Sara be erased, would remain in the past which would probably be sometime around the 40s/50s. Then she continues to be a vigilante and is found and recruited by the Justice Society of America and serves with them for a time, but would retire before 1956 before their "disbanding" after meeting Laurel and Sara's grandfather and having a daughter also named Dinah, who will then go on to meet Quentin Lance and have two daughters with him named Laurel and Sara. What would be cute is if the show featured an elderly Dinah Drake meeting her newborn granddaughters and suggesting their names. As an added bonus if Dinah, provided she's still alive by the 90s, arranged Laurel's first meeting with Oliver as children as Laurel mentioned in 3x21 that she and Oliver had been friends since childhood.
This may be a stretch and maybe overthought, as I have a tendency to do with these posts, but I think this would be the most awesome way to tribute the comics while still adding their own creative touch. It would also be good story material for Sara who has been lecturing Martin Stein about having a daughter as a time aberration, only to later learn that she herself and her sister are also aberrations of the timeline which may make her re-evaluate her perception of what timeline is correct. Some could argue that Dinah needs to stay so she and Oliver can be together to have the traditional Green Arrow x Black Canary relationship, but honestly that wouldn't work for me. They already screwed that up by killing Laurel so I'd find it distasteful to pair her and Oliver together. Plus, quite frankly, I don't think Oliver is her type. If anyone Diggle seems to be more her type or at least someone from a military background like him, no I don't meant Diggle himself as I am aware Diggle is married.