First of all why should he care for a man who tormented him for years , humiliated him Infront of everyone.
Second he could not possibly do anything for harry at that time. He was the target for voldermort. Asking voldermort to spare harry was like asking for a death sentence.
Secondly even when he did went to Dumbledore he asked for lily because she was important to him. James and Lily were Dumbledore people. He ought to protect them without Snape asking for it.
u/Awkward-Student-8764 — 8 days ago