The cause was believed to be a heart attack, the Argus Leader of Sioux Falls reported.
Lust, 53, was most recently serving as a partner of a law firm in Rapid City, according to the newspaper.
He served two stints in the South Dakota House of Representatives, serving from January 2007 to January 2015, following his first election victory in 2006.
David Lust, a former South Dakota state lawmaker who died Friday at age 53, was a married father of four children.
After leaving public office, Lust returned in September 2016, being appointed by then-Gov. Dennis Daugaard to succeed state Rep. Dan Dryden, following Dryden’s death from cancer. Lust served until January 2019.
South Dakota Gov. Kristi Noem, a Republican who served alongside Lust when she was a state legislator, told the Argus Leader that she remembered Lust as an effective lawmaker who showed commitment to criminal justice issues.
“He and I got elected together and we were both whips at the same time,” Noem told the newspaper. “He was a great legislator and a serious legislator, but also the kind that everyone could approach. He was a fantastic man.”
U.S. Sen. Mike Rounds posted a remembrance of Lust on Twitter.
“David Lust was a true public servant, a brilliant legal mind and a devoted family man,” Rounds wrote. “His thoughtful leadership made a lasting impact on the community of Rapid City and the state of South Dakota. Jean and I lift up Becky and their four children in prayer.”
Daugaard also spoke of Lust’s commitment to public service.
“We didn’t always agree on things, but he was very professional,” Daugaard told the Argus Leader. “I always respected and admired him, and I liked him a lot.”
Lust, a graduate of Dartmouth College, leaves a wife and four children.
The Associated Press contributed to this story.