Looking in 8-10 phone books, I didn't find any listing for "Hawthorne Bar"

Here's what I did find...

1931

Pete Castellini had a pool hall on E Street, phone number 38

1938

Pete Castellini had a pool hall on E Street, phone number 38 (which is the same number as the number on the matchbook)

1945

Pete Castellini's home number was 38, the pool hall was at 501 E Street and the phone number was 43

1955

The Hawthorne Club was listed at 501 E Street

This ad, from 1955, says the Hawthorne Club has been in Hawthorne for 25 years