Not really. In this case, it's just (simply) being used as an intensifier. It's quite a common usage. For example: He just won't listen to me. He just gets on my nerves. I just love your earrings. 'Just' makes the sentiment stronger.

Well, more like 'simply' or 'even'. 'Just' can mean 'really' but if I swap 'just' for 'really' in your sentence, it wouldn't mean the same thing exactly. 'Really lose it' would be stressing the intensity of the anger, but 'might just lose it' shows how very close to breaking point the writer is.

I wouldn’t say it is intensifier, exactly. ‘To ‘just’ do something’ here suggests that the something is unlikely or surprising. You are describing something in an extreme way that isn’t normal. I just hate Shakespeare. (Most people wouldn’t describe their feelings in such an extreme fashion) I’m just smarter than you. (It’s a rather sweeping statement that sounds rather impolite, so we normally wouldn’t say it)