I think Lorraine bought her mother stockings with the Pigman's money because she knows her mother needs some, and, despite their differences, she loves her mother and wants to help her out.
Lorraine's mother puts her daughter down and is unnaturally suspicious of everything she does, but Lorraine understands that her mother, a single parent, really does have a hard life. Just the other day, when Lorraine asked her mother for money for sophomore dues, her mother had ranted about how it isn't easy "for a woman to support a kid by herself". She had complained that she "couldn't even afford to get (herself) a pair of nylons, showing Lorraine her only pair that had "so many runs you'd think a cat chewed them" (Chapter 6). When the Pigman takes John and Lorraine shopping he is thrilled to be able to buy them things, and when he presses Lorraine to get something, they just happen to be passing through the women's underwear section in the department store. The saleswoman urges Lorraine to look at "some lovely nylon stockings", so Lorraine embarrassedly says she will take one pair, only to find they come in "three-pair packages" (Chapter 8).
Lorraine fabricates a story for her mother to account for how she got the money to get the stockings, and her mother does indeed question her suspiciously about the gift. Lorraine can tell, however, that her mother is thankful in her own way, and she is gratified (Chapter 10).