The Lackadaisy Speakeasy is an underground bootlegging operation established by Atlas May in 1920. By 1927, following Atlas's death, Lackadaisy is in extreme decline and is owned by Mitzi, Atlas's widow. 
"Growltiger" establishes that one can reach Lackadaisy via a secret door in the pantry of the Little Daisy Cafe, located at surface level immediately above Lackadaisy. There is also a trapdoor in the Little Daisy garage that can be used to get into the caverns connected to Lackadaisy.
Lackadaisy is built within and adjacent to a number of limestone caverns.. The caverns themselves are first properly seen in "Deadlock". There are at least three passages adjacent to each other. One appears to terminate at a closed door; the storeroom is located off a passage to the immediate left.
The Lackadaisy pin is a lapel pin worn by those who work at or otherwise have been invited to Lackadaisy. The pin is in the shape of the suit of clubs.. In "Surreption", Ivy gives Freckle a Lackadaisy pin.
In "Malarkey", Mitzi mentions a storeroom, reachable via the caverns, where firearms are kept. Retreating from the pig farmers, Mitzi, Freckle, Rocky and Zib run for the storeroom in "Skedaddle". The storeroom is located behind Lackadaisy's stage, to the left. "Deadlock" reveals that the storeroom has been unlocked and emptied of firearms...and cleaned...sometime prior.