It wasn't a surprise that Lydia couldn't help Jack train any special techniques or fighting style, because she knew none. She was fast, strong, determined, fearless, and reckless. She was the exact opposite of him, who always plans ahead, sets traps, and tries to gain every possible advantage.
Jack would pick a lock open; Lydia would smash it. Jack uses sweet words and blackmail to get someone to talk, while Lydia would just cut their fingers off. Jack would try to find the secret words in a devil's contract to outplay them, while Lydia would just walk to the devilish bastard and punch them in the face.
Maybe that was their strength, the straight forward Lydia and the shifty Jack. He could teach her how to me more subtle in her style, and she could teach him how to be more aggressive. Together, they might reach the level of rabid violence and malevolent cunning Arad could pull.
