A two-time All-Star, Lucroy was hitting .242 with seven homers and 30 RBIs in 74 games this season. He joined the Angels in December after spending the 2018 season with the Oakland Athletics.
Lucroy had been reinstated from the injured list Wednesday after being injured in a home plate collision with Astros outfielder Jake Marisnick. Lucroy suffered a concussion and broken nose and missed 18 games.
Stassi, 28, had played in parts of every season with the Astros since his debut in 2013. He is batting .167 in 31 games this season after playing in a career-high 88 games in 2018.
Left-hander Adam McCreery cleared waivers and was outrighted to Triple-A Salt Lake.
The Associated Press contributed to this report.