What happens if the hero group is attacked by a Lt. and:

1. they flee: Are they still at their position were they were standing or are they moved to Talamir?

2. they are killed: Is the game week over for them so that they actually loose one week without doing anything?

The rules for endings of encounters are clear for a "normal" encounter and even for an Lt. encounter started by the hero group, but I am not sure for the Lt. encounter started by the Lt.

pretty sure its the same rules no matter who attacks.

The rules do not differentiate on who started the battle. The end conditions are all the same.