I have made the same observation. I believe a big reason for the connection is that socialists, mobsters, and lawyers all historically have something in common: labor unions. The history of this can be traced back to the emergence of communist-agitated labor violence in the 19th century. Moving towards the present, a key figure in forging such links was Sidney Hillman, one of FDR's major links with organized labor and organized crime:
John T. Flynn, The Roosevelt Myth, Chapter Eight - The Shock Troops of the Third New Deal
There is no doubt that Hillman was one of the first labor leaders to use the goon as part of his enforcement machinery. In 1931 a garment manufacturer in Brooklyn named Guido Fererri got into a bitter quarrel with Hillman's Amalgamated and was threatened by one of its officials. A few days later Fererri was found shot to death on the street. At the time a notorious character named Louis Buckhalter, known as Lepke, was officiating as slugger and goon for a labor union and Lepke was suspected of this crime.
The Last Days of Lepke Buchalter, et al
During the two-day reprieve, the New York newspapers ran wild with speculation as to what Lepke had to reveal. Chief among the rumors was that the mob boss could provide information on Sidney Hillman, the president of the Amalgamated Clothing Workers of America. Hillman was a member of President Roosevelt’s wartime administration, and his inner circle. With Hillman’s connections to organized labor, Dewey, it was believed, could link him to Lepke and parlay this information into a corruption scandal to hang over the Democrats in the November 1944 elections.").