Some info and photos are from Find a Grave

https://www.findagrave.com/memorial/6025466/lindsay_crosby

From Wikipedia (English):

Lindsay Harry Chip Crosby, Sr. (January 5, 1938 – December 11, 1989) was an American actor and singer.

Early life

Lindsay Crosby, son of Bing Crosby and Dixie Lee, was born in California and named for his father's closest friend and Thoroughbred horse racing partner, Lindsay Howard. He was educated at Loyola High School, Los Angeles. He was remembered by his friends for having a special laid back and clever wit like his father. He performed with his brothers Gary, Dennis and Phillip Crosby as the Crosby Boys during the late 1950s in nightclubs and on The Ed Sullivan Show.

Death

The Crosby Boys own inability to cope blighted their lives. They were greatly affected by their father's alleged emotional and physical abuse and mother's decline into alcoholism and a premature death from cancer. Heavy drinking and their emotional problems took their toll. Lindsay died from a self-inflicted rifle shot to the head. He was 51. A family spokeswoman said Crosby shot himself to death in a Las Virgenes apartment after learning that the inheritance he relied on to support his family was gone.[1] His distraught brother, Dennis, never recovered from Lindsay's death and also committed suicide with a shotgun in May 1991.