Lyra Surrel is a scientist from Los Angeles. Jack Deth met her in the fourth film while visiting a bar. She later turned out to be one of Jack's new supervisors, and she gave Jack some new weapons, including a sharp switchblade, a new gun and an improved long-second watch with a rechargable cell, to help him on his next mission.
Jack met another Lyra in Orpheus, who had a totally different attitude, and she did her best to try and please Jack by order of Lord Caliban. Eventually, Jack grew tired of her feebleness and told her that to be happy around others, she had to find happiness within herself.
Jack inpregnated her, although he eventually returned to LA with Prospero, so little became of their relationship.