I'm usually not one to speculate or hypothesize much but after watching the end of the morning session again and the timing of the crying, then Baez trying, and finally after several objections, asking Lee if there was any other reasons why he was upset I've come up with a thought.
Lee started crying during a sidebar, not testimony. The sidebar was involving Baez trying to go a certain direction with his questioning and the state was objecting. I suspect Lee knew the direction the questions were about to go. He knew the answers he was supposed to say and possibly had agreed to them prior to taking the stand. On the stand he just couldn't do it and that is when he started crying.
Baez came back asked the question, he answered he was upset about being left out.
That WAS NOT the answer Baez was after. If it was the answer he was expecting he would not have kept asking if there was another reason. Finally, Lee said "no". I think there was a different answer Lee had agreed to give and just couldn't bring himself to do it on the stand and hence, the tears. He could not give the lie on the stand that they wanted him to give.
IMO <removing tin foil hat now>