I got out the phone books

1939-No Western Club listed in Lovelock

1945-Western Club, Cornell, phone 169

1950-Western Club, 1025 Cornell, phone 333
Western Grill, 1035 Cornell, phone 281-J (probably not relevant, but...)

1951-Western Club, 1025 Cornell, phone 333
Western Grill, 1035 Cornell, phone 35

1952-Western Club, 1025 Cornell, phone 110
Western Grill, 1035 Cornell, phone 35

1955-Western Club, 1025 Cornell, phone 110
Western Grill is no longer listed

1956-Western Club, 1025 Cornell, phone 110

1957-Western Club, 1025 Cornell, phone CR3-2219

1959-Western Club, 1025 Cornell, phone CR3-2219

1963-Western Club, 1025 Cornell, phone CR3-2219

1964-Western Club, 1025 Cornell, phone 273-2219

1966-Western Club, 1025 Cornell, phone 273-2219

1972-Western Club, 1025 Cornell, phone 273-2219

That's as far as our phone books go.

I'd say it's a pretty safe bet that your matches were made between 1957 & 1963 . (I'm amazed at how often they changed phone numbers in the early days!)

I couldn't find any helpful display ads in the yellow pages.

Fuller's index says The Western Club was licensed for craps, 21 and roulette.