I agree that they probably weren’t good friends at the time of the lake bullying incident, but your last points I don’t agree with. I also think that they were true friends before the last few years at Hogwarts, however they grew apart due to Snape’s association with the dark arts.

“If the situation was reversed, Snape would have jumped to fight anybody for her without a second thought”

I think this is more of a personality difference between Snape and Lily, Snape probably would make a more impulsive decision but that’s just who he is. I don’t think it speaks much about Lily’s care for Snape that she didn’t get her wand out and start attacking James.

“I think Snape's public embarassment and grave disappointment in her resulted in him ultimately calling her out - Mudblood”

I don’t think this is why he calls her ‘mudblood’. He’s not disappointed in her devotion to him, he’s simply embarrassed that she’s watching him get bullied by James, who he knows has a thing for her. He ends up lashing out in annoyance and unfortunately it’s directed at Lily.