"one thing I do not understand is why would Joe be angry at Lisa when he finds out about Dinah. he knows that her morality is as he described as enlightened self-interest and he could have found out about her with all the resources he have if he did not let said teenagers take charge when he KNOWS she is fucking with him.":
Joe would be angry because emotional reactions are not based on logical processing of facts. It would be as simple as hurt girl = outrage. Also, Joe being angry at himself because of how he handled the situation doesn't mean he won't be angry with Lisa for how she handled the situation. Lisa having terrible moral standards which are reinforced by her actions in this matter would make Joe more angry, not less.
[Follow-up]
I'm not sure why you're fixating on the fact that Joe will feel anger when he learns about a child suffering. Regardless of the details of the situation or the nature of the people involved, anger would be a very natural reaction towards everyone involved. That includes Coil, Lisa, and even himself. Yes, Lisa has compromised morality, but there are levels to that. He has had no indications that she would be alright with something of this nature, and frankly she won't be. Once she finds out she will be horrified. That will mostly be because she understands the situation, her role in it, and how Joe will react, but she's not going to be trying to say Joe has no right to be upset because he should have known what he was getting into. Once again, anger is an emotion, and emotions aren't based on logical assessments of a situation. If you're asking what Joe will do, that's a different story, but no matter what action he decides to take, feeling angry about the situation will be a very natural reaction.