Are Robert Pattinson and his new lady lover taking the next step in their relationship? Are Robert Pattinson and his new lady lover taking the next step in their relationship? Robert Pattinson Wants To Show Off FKA Twigs To The World? On Monday, E! News reported that the Twilight star and his British singing girlfriend FKA Twigs went furniture shopping last weekend for the new house that the actor bought for himself in Los Angeles.