We’ve withheld presenting any consideration the Clinton/Lynch meeting in Arizona until AG Lynch presented her thoughts/explanations on the event.
SHE DID THAT TODAY.
As you can see in this interview (below) directly discussing the matter Attorney General Lynch goes to great lengths to walk through the parseltongue politispeak surrounding her meeting with Bill Clinton.
Pay attention to the phrases she is using.  Specifically note the frequency of:  “raises questions and concerns”, and “casts a shadow over how this case may be perceived”.  Those phrases alone make the ethical case for recusal.
However, against the call for her to recuse herself the next key phrase to focus on is:  “would mean that I wouldn’t even be briefed on what the findings were, or what the actions going forward would be.  And while I don’t have a role in those findings or making those recommendations on how to go forward, I will be briefed on it, and I will be accepting their recommendations.”

There it is. The real motive behind AG Lynch refusing to recuse herself (now that she was caught intentionally meeting with Bill Clinton) can be found in that explanation:

“[recusal] would mean that I wouldn’t even be briefed on what the findings were, or what the actions going forward would be.  And while I don’t have a role in those findings … or making those recommendations on how to go forward, I will be briefed on it, and I will be accepting their recommendations.”

Lynch, a political appointee, will not recuse herself because that would mean she would be cut out of the loop, and the information to the Clinton camp -via the White House- would go dark.
President Obama and Hillary Clinton would lose their source to give them information on how the investigation is going.  They would lose the advance notice.  They would lose any control over what would be coming toward them.
That’s the problem.
That’s why Loretta Lynch will not recuse herself.