I am sorry to hear about Max's strange behavior lately, unusually aggressive with his housemate, lethargic, barking at seemingly nothing and just not himself.
When animals suddenly change their attitudes toward one another it means that something has changed. Either there is some sort of stress in their lives, resources (including time with you) are less or someone isn't feeling well.
So ideally both should have a thorough physical examination, urinalysis and bloodwork to make sure all is OK. Animlas are very good at picking on the one who is weak in the group. Dogs are very keen at picking up a change in body odor which can signify sickness.
It's also possible that Max has an undiagnosed health problem which is making him less tolerant of his housemate and is changing his perception of his environment. He is an older fellow and as such organ failure is possible. As organs fail and metabolic wastes build up their brain function becomes abnormal. Unfortunately Boxers as a breed are prone to brain tumors and heart disease. Heart disease can lead to episodes of hypoxia and "feeling funny" which Max may blame on his housemate, or simply take his frustration out on her. Of course brain tumors can affect thinking.
Make sure their urine is checked for any signs of crystals or infection and cultured to make sure a subclinical low grade infection isn't part of the problem. Bloodwork to look for internal organ disease and hypothyroidism is advisable too. I know that he was previously diagnosed with low thyroid function, and perhaps his medication dose needs to be adjusted. Low thyroid function can change behavior and thought patterns and lead to "mental dullness" so would explain his "trances".
In the meantime I recommend that you keep the two separated for her safety, as this seems to be worsening. Should an attack occur when you aren't home the end could be disaster.
Please let me know if you have any further questions.