Is Lily Potter really muggle born?

Here's some speculations about wether Harry's mother Lily Potter realy is muggle born

• I see in multiple areas where you think that Lily Potter is Muggle-born. Is there anywhere in the books that actually says that? I realize in book 2 Harry says she is muggle born to Tom Riddle, but of course he would think she is muggle born I ask that because I suspect that Lily and Petunia's parents were magical people. I keep thinking that maybe for some reason, Lily's parents hid their magical background from their kids. In Book 1 when Hagrid is in the house on the rock in the sea, Petunia says that her parents were so proud to have a witch in the family.
I see no reason why muggles would be so proud about having a witch in the family. I suspect many muggles would react more like the Dursley's if they found out they had a witch in the family. I think the reason why Petunia is so bitter towards Harry, Lily and the magical world in general is because her parents knew for a long time that Lily was a witch, but Petunia turned out to be a squib and therefore treated Lily differently (and probably better) than her sister Petunia.
In my theory I am not sure of why Lily's and Petunia's parents would hide their magical abilities. The only thing I can think of would depend on when Voldemort came to start his terror. If Petunia and Lily were born after Voldemort came to power, then maybe Lily and Petunia's parents hid their magical abilities to protect their children (Elangomatt)

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