We're not sure that anyone could actually "take the place" of Lefty who, love him or loathe him, was pretty much a one-of-a-kind kinda guy. If you mean who replaced Frank Rosenthal at the helm of the Stardust (his de facto role, despite various euphemistic titles employed to get around Lefty's inability to own a Las Vegas casino license, due to his well-publicized shady past and ongoing association with unsavory mobsters), that's another story.
After the 1982 assassination attempt on his life, which was the subject of Sunday's QoD, Lefty took the hint and left Las Vegas not that long after. In 1988 the Nevada Gaming Control Board placed him in the notorious Black Book, which banned him from even entering any casino here, although he was already residing in Florida by that point.
During Lefty's reign, the Stardust had been owned by Allen Glick's Argent Corporation, which purchased it 1974 using loans from the Teamsters Central States Pension Fund and was a known front for various Midwest organized-crime families, who infamously "skimmed" the joint for millions of undisclosed dollars.
Argent was forced out by the FBI and in 1979 the Nevada Gaming Commission licensed two local casino entrepreneurs named Al Sachs and Herb Tobman to purchase the company's assets, which also included the Fremont downtown. However, the mob influence remained and in 1984, a couple of years after Lefty's departure, Sachs and Tobman's Trans-Sterling Inc. was fined $3 million for skimming. It was the highest fine ever issued by the Nevada Gaming Commission and Sachs and Tobman were both stripped of their gaming licenses, leaving the Stardust in search of a new, clean owner.
That figure came in the form of locally based casino owner and legitimate businessman Sam Boyd, whose gaming company purchased the Stardust in March 1985 and found it to be an unexpectedly profitable proposition, once the illegal skimming was removed from the equation. Boyd Gaming was still the owner of the 'dust when it permanently closed its doors to the public on November 1, 2006.