Suppose I am being questioned by the police about my whereabouts when a crime was committed. The lecture finished at 1 p.m. and a computer was stolen from the school at 1.30 p.m. I assert that I was not in the school grounds at that time because straight after the lecture finished, I went home. Hence, I would say to them:
I went home straight after the lesson.
Say the crime was robbing a small shop a few blocks away from the school at 1.30 p.m. I finished school at 1 p.m. so I could have done it after the lecture had finished. But I assert that I went straight home, not stopping off or going any other place on my way home. I would say to them:
I went straight home after the lesson.
The position of 'straight' depends on whether I am stressing that I went directly to my home, or that I went home directly after the lecture finished.
Student or Learner