Violet Polley was murdered on Christmas Day, 1929.

Lilly's phone call outside the restaraunt:

After her heated exchange with her mother, Lilly goes outside and spontaneously calls a man who is never mentioned by name, but considering Lilly's conversation with his machine, it is most plausibly ADA Kite (last seen in Season 1).

During Season 1, Kite aggressively tried to court Lilly, but for reasons not quite clear at the time she always seemed either distant or passive about the relationship. Eventually Kite stopped calling when he figured out that she wasn't ready for a relationship---with him or anyone else.

However, after two years, it is made relatively clear why Lilly rejected Kite's proposals---she was afraid of ending up like her sister Christina (a cheap fling in trouble with the law) or like her mother (an alcoholic who routinely choose the wrong man).

Whether or not Kite makes an appearance in a future episode concerning Lilly's call/confession remains to be seen.

Lilly takes the Polley case despite the backlog of more recent cases because, unlike the rest of the team, she can empathize with the victim's great-granddaughter when she says that the women in her family seem to end up screwing their lives up. Lilly takes this comment personally, considering her upbringing at her mother's guidance and the fate of her sister.