Could you specify what you mean by this? The way your phrasing the question makes it seem like you're here looking for someone to do your homework.

I was not aware the Korean war was lost. While you can certainly say that the USA/ South Koreans failed to achieve total victory, you could just as fairly say the same thing about the North Korean/Chinese communists.

Add in the simple fact that there has been no formal peace agreed to and there is still a heavily guarded demilitarized zone between the two koreas, and I just don't think you can support your assertion that the Korean war was lost.

The original US mission in the Korean war was to stop Communist aggression that manifested itself in the Soviet-backed invasion of South Korea. Once the North Korean invasion forces were crushed and the South was liberated, the mission was considered a success.

When the military command on the ground decided to move north of the 38th parallel, the war evolved into a different conflict altogether. When the Chinese Communists entered the conflict, it changed again.

Rather than "losing" the Korean conflict, the political leadership decided the costs of containing the Chinese in China were not worth any benefit gained by freeing North Korea from Communist domination. Once the battle lines returned to the general areas of the prewar border the US decided to accept the reality on the ground.

The Americans had the power to destroy the Chinese forces and killed an estimated 1 million ChiCom soldiers. The Chinese had an unlimited capacity to send in replacements, however, so it was decided Korea was "the wrong war at the wrong time in the wrong place."

The impact of the lessons learned in Korea on the Vietnam War was basically a guarantee the US would never attempt to invade North Vietnam based on a real fear the Chinese Communists would again intervene. Containment, not conquest, became the goal.