"He is receiving excellent treatment at Palmdale Regional Medical Center and anticipates a full recovery," the statement from Chief of Staff George Andrews said.
Lackey, 61, represents the 36th District, which covers the Antelope Valley and the Santa Clarita Valley.
On Monday afternoon, Assemblywoman Autumn Burke, who represents California's 62nd Assembly District, which includes parts of the Westside and South Bay, confirmed she had tested positive for the coronavirus.
The California state Capitol in Sacramento will be closed until early next week after five Assembly lawmakers and staff tested positive for COVID-19.
Coronavirus: California state Capitol closes after Marina Del Rey assemblywoman tests positive for COVID
California Assemblywoman Autumn Burke speaks out after testing positive for COVID