Lisa Vanderpump knows James Kennedy primarily through his family, specifically his parents, whom she met through a mutual friend.
Lisa met James's parents, Andros and Jacqueline Georgiou, a few years before James began working for her. This introduction was facilitated by Bruno Tonioli, a well-known judge on Dancing with the Stars, who is an old friend of Lisa's. Prior to this, Lisa had a prior, albeit vague, acquaintance with James's father, Andros, and her husband, Ken Todd, also knew Andros loosely.
The connection therefore stems from a long-standing friendship between Lisa and Bruno Tonioli, which then branched out to include James Kennedy's family, eventually leading to James's involvement with Lisa's businesses and his presence on Vanderpump Rules.