My 10 year old won't stop lying.

I'll start off by saying, my daughter has always been insecure for some reason none of us understand. We feel like we give her everything she wants pretty much. Of course within reason, and we never reward bad behavior. She is not an only child, she has a little sister.. and we personally feel we treat them 100% equal. Her little sister is her polar opposite. Anyways, she keeps lying to her best friend/neighbor. It's not in a playful way at all, like "tricked you!" Or "just joking!"..she lies and sticks to it. Our neighbors make more money than my husband and I combined, so they can afford to go all these places and their kids brag a lot. We can really only afford smaller places like the zoo, shedd, ect. So I could understand if my daughter was insecure that her friend gets to go to Disney twice a year, and she's never even been. She's lied to her friend saying we were going to these outlandish places for spring & winter break when we obviously weren't. She's said we are getting her a cell phone, and when confronted..she literally said to my face "yes you said I was getting one soon" when I didn't. Her lies started off like this, materialistic (which is why I figured it was due to not having the same lavish life as her friend) and now she's lying about such dumb stuff. She lied to her friend and said her cousin has 6 dogs and a jumping squirrel ? When they have 2 dogs..and no jumping squirrel.. so when I confronted her in front of her friend, she was determined to not look like a liar..but covering up her lie with MORE lies! Telling her friend "well no I didn't say they had that many dogs..i said I think they were getting more dogs..and i never said they had a jumping squirrel" meanwhile the friend is looking very irritated and insisting that she in fact told her these things and now she's lying again. There's a million more things she's lied about that were so random, and the weirdest things to lie about? But how do I stop this!? I've talked with her numerous times in a loving, calm way about it, but everything I say just goes over her head..obviously. I told her I'm just trying to understand why she lies about these small things and she basically says she's not lying and sticks to her guns. I'm at a loss..has anyone else dealt with this and how did you fix it? It's embarassing when the neighbors mom keeps asking me if things my daughter said to hers is true and it clearly isn't.

--just need to add that I never intentionally tried to "shame" my daughter on purpose. Her friend keeps asking me in front of my daughter if these things are true..I just don't know how to respond anymore..and that was one of my last ditch efforts to get her to stop lying..to say in front of her friend that it wasn't true. But I never made her feel bad about it. I just wanted to show my daughter I will not back up her lies. And I already stated that I've talked to her one on one numerous times asking why she says these things, in a calm loving way. I make the communication very open for her, even admitting I said some white lies when i was her age, too & explaining why I did it.