Luco Palma was born on June 27, 1950, in Celie, West Germany. He enlisted in the U.S. Navy on December 30, 1968, and completed basic training at NTC Great Lakes, Illinois, in April 1969. Palma next attended Basic Underwater Demolition/SEAL training with Class 053 at NAB Coronado, California, from April to November 1969, followed by service with UDT-13 at NAB Coronado from November 1969 until he was killed in action while deployed to South Vietnam on September 18, 1970. During this time he participated in the recovery of APOLLO 13 aboard the amphibious assault ship USS Iwo Jima (LPH-2) from March to April 1970, and then deployed to Southeast Asia on September 1, 1970. He was posthumously promoted to Petty Officer Third Class after his death.

His Navy Achievement Medal Citation reads:

For professional achievement in the superior performance of his duties while serving as a member of the Underwater Demolition Team THIRTEEN detachment embarked in USS IWO JIMA (LPH-2) for the APOLLO 13 recovery operation from 31 March to 25 April 1970. As a member of one of the swim teams at the scene of the splashdown, Seaman Palma performed his assignment flawlessly. He executed every task in the vicinity of the command module with rare skill and precision, ensuring the recovery of vital equipment. Seaman Palma's resourcefulness, professional skill, and devotion to duty reflected credit upon himself and were in keeping with the highest traditions of the United States Naval Service.

His Vietnamese Military Merit Medal Citation reads:

Serviceman of courage and rare self-sacrifice, he displayed at all times the most tactful cooperation while aiding the Armed Forces of the Republic of Vietnam to repel the Red Wave undermining South Vietnam and Southeast Asia. With a ready zeal and commendable response, he fought on to the end in every mission and set a brilliant example for his fellow soldiers. He died in the performance of duty. Behind him he leaves the abiding grief of his former comrades-in-arms, Vietnamese as well as American.