Lloyd, 34, was offered a date with the superstar after he spotted her at a Hollywood party when she was just 18 and he 25 - before the pair starred together in A River Runs Through It and before Pitt became a household name.
She explains, "I was with my sister CHARLOTTE at a party thrown by George Michael. Sinitta, the singer, came up to me and said her friend Brad really wanted to me to go over and talk to him as he would like to take me out.
"I hadn't seen him but I thought the name Brad sounded so naff and my sister wanted me to take her home as well, so I didn't bother.
"But I was kicking myself the next day when I was shown a picture of him."