We did not lose the Korean War. The N. Koreans and later, the Chinese, invaded the South and drove the UN troops (Mostly American troops stationed in Japan and poorly trained) and the ROKs down to a small part of the South. Their goal was to take over the South and unify the country under communist control, and they almost did it.
However, we fought back and pushed them back across the 38th parallel (N. Korea/S. Korea border) and then almost into China until Truman stopped MacArthur from invading China.
The end result was a stalemate that kept the South free. So the North did not accomplish their goal of unifying the country under communist control.
Consider the fact, also, had we not dropped the A-Bomb on Japan, the most likely result would have been Japan being divided just like Korea, and most likely a war instigated by the Communists to take all of Japan.
“...until Truman stopped MacArthur from invading China.”
MacArthur did not want to invade China, but he wanted to destroy the NORKS and drive them into China. The only action MacArthur ever contemplated vis-à-vis China was to bomb strategic sites, and at that it was a musing rather than a serious idea.
MacArthur first got into trouble with Truman when in the fall of 1950 he told Truman that it was highly unlikely the Red Chinese would intervene, contrary to what intelligence reports suggested, and which MacArthur ignored.
X Corps, under the command of the insufferable General Edward Almond, a MacArthur toady, was largely responsible for the debacle at Chosin Reservoir, in which the grossly outmanned US Marines performed valiantly, thanks to the leadership of Marine general Oliver P. Smith. The breakout from Chosin should be studied by any serious student of history.