ref : Julia's Eyes Explained
Isaac was murdered. As you pointed out rightly, at that moment in time Isaac is worried for Julia and is trying to be as protective as possible so that she doesn't lose her eyesight trying to chase ghosts.
While the suicide note suggests murder, it was probably planted there
by Ángel. Ángel has been systematically removing all of the evidence
connecting him with Sara. Isaac was going to get his hands on the
surveillance tapes that could incarcerate Ángel. Isaac had no reason
to commit suicide because he was not the one in the surveillance
tapes. Also, Isaac was found hanging in the exact same way Sara was
found. We know Ángel killed Sara. As for the phone records where Isaac
has made multiple calls to Sara over the past 6 months. Well, those
are real, they were actually having an affair. Isaac loved Julia and
didn't kill himself.
Towards the end Lia tells Julia this:
ref : Julia's Eyes Dialogues
Do you really think Isaac killed himself? He loved you.
Sara more. They didn't want to worry you.
That's why they kept
you in the dark. Sara told me.
The monster forced him to write
the suicide note.
Lia seems to know a lot in this scene. Even regarding the pictures on the wall or about the keys and that the care taker was actually the invisible man. She's been snooping around on her own finding things. From this it looks like Angel had gotten that note created one way or another. Either by force or by forging.
In summary, Isaac was killed by Angel. The suicide note was forced or forged.
The phone calls were real because Isaac and Sara were actually having an affair.