Quick searchings by Cepheus and Aiken reveal that the Blacklilies tend to focus their efforts on the dock, and used to congregate at a bar known only as the "Ship's Wheel". However, some weeks ago, the 'Wheel was cleansed of Lily influence after a massive barfight that left several 'lilies dead.
Solange and Pendrake could fill you in on that.
As for the actual 'lily lair, they tend to just get together in seedy bars throughout the dock district. The children know of several names that are friendly to lilies - "The Crab Street Digs", and "One Night's Rest" - the latter a combination bar/brothel.
Major 'lily gatherings are done in secret, but Cepheus (with Aiken's aid another check) is able to direct the children's inquiries in many different directions to eventually come to the conclusion that many blacklilies are seen (without their scarves) at a two-floor manorhouse on Merchant's Avenue. This home, Aiken discovers after paying for a few drinks at a well-to-do inn for Merchant folk, belongs to Lady Ciara Ilvassa - the only daughter of the late Korben Ilvassa (a fairly well-off merchant, though not wealthy by any standard).
This gathering of information takes four hours, during which time Solange and Pendrake seem to make little headway in the search for an addition to your party (I forgot about the Mega Adventure!). By the time you all gather once more, it is perhaps six p.m, and the rains drown the cobblestones once more.