English Translation
She used to date him.
Here we need to distinguish “Būtasis kartinis laikas” and “Būtasis dažninis laikas”.
Used to refers to Būtasis dažninis laikas, as it emphasizes regular repetition, habit, or cyclicality of an action, and sentence should look like “Ji susitikinėdavo su juo”.
When we talk about Būtasis kartinis laikas, it indicates a process that took place during a certain period in the past. So the translation should be something like “She was dating him” or “She dated him”.