Plato, who is best known for her work on the classic TV sitcom "Diff'rent Strokes," died of a prescription drug overdose in 1999 and her death was ruled a suicide. She was 34.
Her former mother-in-law, Joni Richardson, told People.com the cameraman and aspiring songwriter had long struggled with his mother's death and killed himself May 6. His body is to be cremated and no memorial is being planned.
"It's a shame that such a talented human being would do this with his life," Richardson told the Web site.
"He had all the opportunities in the world and we just can't understand it," she added. "Our lives have just been wrapped around him. ... It's just devastating."
The Oklahoman said Lambert committed suicide in Kellyville, Okla., two days before the 11th anniversary of his mother's suicide.
Plato died while visiting Moore, Okla.