Bostock was drafted by the St. Louis Cardinals out of Manual Arts Senior High School in Los Angeles, California. However, he chose to not sign with the Cardinals, attending California State University, Northridge from 1970 to 1972. He was an All-Conference player in the California Collegiate Athletic Association both of his seasons at Northridge, hitting .344 as a freshman and .296 as a sophomore, leading CSUN to a second-place finish at the 1972 Division II College World Series. Bostock was then drafted by the Twins in the 26th round of the 1972 amateur draft.

A fine center fielder, Bostock finished fourth in the tight American League batting race in 1976, his first full season in the majors. After finishing second in the league in batting in 1977, Bostock became one of baseball's earliest big-money free agents, signing with the California Angels, owned by Gene Autry. Bostock almost immediately donated $10,000 of his newfound wealth to a church in his native Birmingham, Alabama to rebuild its Sunday school.

Bostock's 1978 season started off a disaster, with him batting only .150 for the month of April. Bostock went to Autry and attempted to give back his April salary, saying he hadn't earned it. Autry refused, so Bostock announced he would be donating his April salary to charity. Thousands of requests came in for the money, and Bostock went through each of them, trying to determine who needed it the most.

Bostock worked the rest of the season to get his batting average up over .300. On Sept. 23, 1978, with his batting average sitting at .296 after a game with the Chicago White Sox, Bostock visited his uncle in Gary, Indiana. After eating a meal with a group of people, Bostock got in the back seat of his uncle's car. As the vehicle crossed the intersection of 5th and Jackson streets, a car pulled up along side them. The driver got out and fired one blast of a 410 gauge shotgun into the back seat where Bostock was sitting. The shooter, Leonard Smith, did not even know Lyman Bostock. His lethal wrath was intended for his estranged wife, Barbara Smith, who was along with the group as a guest of Bostock's uncle, Thomas Turner, who happened to be her godfather. The blast missed the woman but struck Bostock in the left temple. He died two hours later at a Gary hospital. It was later discovered that Bostock had known the woman in the car for a total of twenty minutes.

Tried for murder, Smith was eventually found not guilty by reason of insanity. Though Smith was jailed awaiting and during his trial and confined for psychiatric treatment afterward, he was soon deemed no longer mentally ill by his psychiatrists, and Smith's total time in custody ultimately amounted to only 21 months. Leonard Smith was released from Logansport State Hospital and returned home a completely free man less than two years after having taken Lyman Bostock's life in cold blood.

In a four-season career, Bostock was a .311 hitter with 23 home runs and 250 RBI in 526 games. A memorial scholarship fund was commissioned in his name, and is annually awarded to a needy CSUN student athlete. In 1981, he became the first person to be inducted into Cal State Northridge's Matadors Hall of Fame.

Bostock is interred in the Inglewood Park Cemetery in Inglewood, California.