The Hard Out Here singer posted a snap of herself cutting a fine figure in a fitted LBD and leopard print stiletto heels.
She wrote alongside the picture: "Just going to the shop, want anything Katie?"
The shot followed a series of angry tweets from the singer, which she has since deleted from her Twitter account.
The mum-of-two then wrote: "Sorry about that, but my babies are a touchy subject and I gave her exactly what she wanted by responding. I am now going to delete it all."
Lily's comment directed at the ex-Apprentice star comes in response to Katie's open criticism at the singer gaining weight after falling pregnant.
"I quite liked her when she was singing and kind of interesting and then she went off to tell us all about being a mother," said Katie, 38, in an interview with Heat magazine.
"She was removing herself from the spotlight because she wanted to be a mother and that largely involved gaining two stone and looking pretty hideous.
"So then she decided that was boring and now she wasn't going to be a mother any more, she was going to be a singer.
"Like Peaches (Geldof), she is just famous for having a famous dad."
Katie has won herself a reputation for venting unpopular opinions and has got into public feuds with Peaches Geldof and mother and daughter Sharon and Kelly Osbourne.