I think I have an answer, but it gets pretty deep in the weeds. But here goes ...

It has to do with the overlap of 4 downtown casinos with similar names and dates of operation, all in the same mid-block area next to the Golden Nugget.

Lucky Strike Club
Per ChipGuide: located at 117 E. Fremont St., open 1952 to 1969, "Slots Only".
Per Fuller's index: same location and dates. It DOES list the following games: slots/21/craps/roulette/keno/bingo. BUT I think I can explain away the live games, below.
Distinguishing features: huge "Lucky Strike Club / Bingo" sign in front and on top of location, sandwiched between Golden Nugget and the Nevada Club.
No chips or tokens (as you correctly say), and their matchbooks only mention slots and bingo. (They do say "casino" too, on one matchbook, but I think that just refers to gambling in general, not live games.

Lucky Casino
Per ChipGuide: also located at 117 E. Fremont St., open 1963 to 1967. NOTE: This is SOME of the same years that the Lucky Strike Club is open. Chips, roulettes, and some interesting Order Cards (more on these later) are shown.
Per Fuller's index: same location and dates. Lists the following games: Slots/21/Craps/Roulette
Distinguishing features: in postcards, the huge Lucky Strike Club/Bingo sign has been replaced by the equally huge Lucky Casino sign. In a photo on Over50Vegas.com, it is shown still sandwiched between the Golden Nugget and (Diamond Jim's) Nevada Club. It's during this latter 5-year period that the location had live games, not the entire period of the Lucky Strike Club that Fuller references above.

Nevada Club (and also a series of chips, including 2 dovetails, that say "Lucky Nevada Club")
Per ChipGuide: 109-113 E. Fremont, open 1953-1955. (The narrative of name changes and owners is a good guide.)

Nevada Club, Diamond Jim's
Per ChipGuide: 109 E. Fremont, open 1962-1969.

For some deeper cross-referenced research on these locations, go to Over50Vegas.com and its' "Listing by Address" page here --
https://over50vegas.com/sitemap-2-address-order.html

Pull up the 4 casinos from the link above:
117 E. Fremont: Lucky Strike Club and Lucky Casino (closes in 1967)
113 E. Fremont: Nevada Club to Diamond Jim's Nevada Club and Lucky Nevada Club (opens in 1967)
The date progression shows these expanding and absorbing into each other, all mid-block, before they are ultimately swallowed up by Golden Nugget taking up the whole block.

Basically, the Lucky Strike Club / Lucky Casino /Lucky Nevada / Nevada Club (including Diamond Jim's) casinos all overlapped these mid-block addresses, expanding and name-changing ... and adding/deleting owner groups, over a 16 year period, 1953-1969. Sometimes with "non-live" games (slots, bingo, keno) and other times, live games (BJ, Craps, Roulette) too.

A final tidbit: Read the Over50Vegas.com narrative on the Lucky Strike Club page. It refers to a familiar casino owner, Milton Prell, operating the Pioneer Club, the Mint and the Lucky Strike Club. Noted on the first order card for the Lucky CASINO's ChipGuide page, you'll see that some 25c small crown "Lucky Casino" chips were delivered to: "Lucky Strike Club, c/o The Mint, 100 Fremont Street, LV"... an illustration of the common ownership/operation of some of the downtown clubs.

Whew! That was a lot!