Lizzy was a homeless woman portrayed by Beth Grant in The One With The Thumb.
Phoebe regularly visits her to give her food and other essentials. When Phoebe's bank account was accidentally credited with $1000 and a football phone, she gave these to Lizzy. As a thank-you, Lizzy offered Phoebe her model XK-7 SatNavBlok Tinfoil Hat, but ultimately bought Phoebe a soda with a thumb in it.