Meeting in the cafe is fine by me~ So how are we going to do with the timeline? I mean, Lili is younger than Vash so presumebly he'd have to had left his biological family (in whatever way you intended him to) when she was young, maybe young enough for childhood amnesia so she doesn't remember him. Wikipedia says: "Childhood amnesia, also called infantile amnesia, is the inability of adults to retrieve episodic memories before the age of 2–4 years, as well as the period before age 10 of which adults retain fewer memories than might otherwise be expected given the passage of time."
Or we could have him have left them later and she has memories of them, albeit vague. What do you think would be best?