Edgar was born in Leadville, Colorado, on the 22nd of November 1944, and he enlisted in the US Army at 19 from Denver, Colorado. In 1967, he deployed to the Republic of Vietnam with the 1st Battalion, 5th Cavalry, 1st Cavalry Division (Airmobile), and it was his actions on the 21st of June that would cost him his life and earn him the Medal of Honor. The citation reads:

For conspicuous gallantry and intrepidity in action at the risk of his life above and beyond the call of duty. Serving as a medical aidman with Company B, Sp5c. McWethy accompanied his platoon to the site of a downed helicopter. Shortly after the platoon established a defensive perimeter around the aircraft, a large enemy force attacked the position from three sides with a heavy volume of automatic-weapons fire and grenades. The platoon leader and his radio operator were wounded almost immediately, and Sp5c. McWethy rushed across the fire-swept area to their assistance. Although he could not help the mortally wounded radio operator, Sp5c. McWethy's timely first aid enabled the platoon leader to retain command during this critical period. Hearing a call for aid, Sp5c. McWethy started across the open toward the injured men, but was wounded in the head and was knocked to the ground. He regained his feet and continued on but was hit again, this time in the leg. Struggling onward despite his wounds, he gained the side of his comrades and treated their injuries. Observing another fallen rifleman lying in an exposed position raked by enemy fire, Sp5c. McWethy moved toward him without hesitation. Although the enemy fire wounded him a third time, Sp5c. McWethy reached his fallen companion. Though weakened and in extreme pain, Sp5c. McWethy gave the wounded man artificial respiration but suffered a fourth and fatal wound. Through his indomitable courage, complete disregard for his safety, and demonstrated concern for his fellow soldiers, Sp5c. McWethy inspired the members of his platoon and contributed in great measure to their successful defense of the position and the ultimate rout of the enemy force. Sp5c. McWethy's profound sense of duty, bravery, and his willingness to accept extraordinary risks in order to help the men of his unit are characteristic of the highest traditions of the military service and reflect great credit upon himself and the U.S. Army.

Edgar was 22 years old at the time of his death and his family received his Medal of Honor from President Nixon on the 16th of October 1969, in a ceremony at the White House. Edgar Lee McWethy Jr is buried with his parents in Pence Cemetery in Baxter Springs, Kansas. His name appears on the National Vietnam Veterans Memorial in Washington DC: Panel 22E, Line 32.