If the Bag is enjoyed by brigands celebrating good fortune after a job, Tymora's Coin is meant to solicit good fortune before a job, usually by a crew of brigands working together. SCAG, the god of luck, is a mercurial and kind figure who is as likely to smile upon a rogue as a paladin so long as they refrain from violence and target the greedy.
The titular coin is Tymora's symbol because sometimes one's fate feels as random as flipping one. The anise and lavender in the punch both carry a blessing for luck, and the lemon wheels represent Tymora's symbol. The number of "coins" that spill from the pitcher into each person's drink represents how much luck the goddess is granting each member of the crew. This can lead to some nervousness if one member of the crew gets no lemons at all.
We leave the reader to speculate what it says about the nature of thieves that the traditional drink before a job is enjoyed by a group and the traditional drink after a job serves only one or two.