There are complicated feelings surrounding Lea and Isa. I think a lot of their friendship was steeped in bitterness following the events that led to them becoming Nobodies, but both of them remember their friendship and how it was in the past. To Saix, he felt as though that friendship meant that Axel was obligated to listen to him and follow his orders.
To Axel, it seemed as though he was just along for the ride. He remembered their past, knew they were friends, so he was supposed to work with Saix.
When Roxas and Xion come into the picture, it definitely opened Axel's eyes that there was something intrinsically missing in his friendship with Saix. To Saix, it became a mix of feeling as though something he felt he was obligated to was taken away and a reminder of what was lost.
It was why I think Saix took so many opportunities to belittle Roxas and Xion and the friendship RAX have with each other. Roxas had no sense of who he used to be, and yet he gained Axel's easy friendship. Xion was just a puppet and yet Axel grew to care about her like a sister. They were nothing to him, but Axel seemed to care about them and that struck a cord in Saix.
Saix needed to return things to status quo so his plans with Axel wouldn't be jeopardized, and clearly he felt jealousy over seeing what he did not have.
The one thing we aren't clear on is when Saix began to fall in line with Xehanort, especially because he was already exhibiting signs of being a Xehanort long before the events of Days. I wouldn't be surprised if Saix didn't start to really fall in line with Xehanort until everything with RAX began, but we can't say anything for certain. What is worse is that we don't really know what Axel and Saix's plans to topple the Organization involved.
Considering everything we know about Saix and Axel, I have always believed that their friendship is meant to represent a broken bond and it is one that likely won't be repaired.
Theirs is a friendship that was once strong becomes abusive and harmful when it is tainted with jealousy and apathy on both sides (Saix being the jealous one and Axel the apathetic one).
When Lea sees Saix as one of the 13 in DDD, I think it isn't him being upset about his friend but rather feeling regret over what has happened. It is in part his actions that caused Isa to suffer the most. Lea was the one who insisted on sneaking into the castle, but it is Isa who gets claimed as a darkness and Isa who had to suffer watching Axel drift away and become friends with some boy with no memories and a puppet.
Now, if Lea saves Isa...I don't think it'll be what we expect. I completely believe Isa will not make it to the end of KH3 alive, but I don't think he will die a villain.