As you said, in English "I'm lost" can be used in two meanings.
Physically "I lost derection."
Emotionally "I don't know what I am doing now and lose the goal of my life"
"길을 잃었어" can be usually used "I lost direction" in phycially and sometimes emotionally.
"길이 보이지 않아" (I can't see the way) mean "I lost the direction of my life" in emotional way.
"어떻게 살아야 할지 모르겠어" (I don't know how I should live my life" can be used in emotional way
"뭘해야 될지 모르겠어" I don't know what I want to do.