No, the Lance is one of the best weapons for chasedown in the game. He needs to get better at using the charge—most monsters really shouldn't be moving again before he can catch up to them. He can go into the charge so fast that it shouldn't be getting away from him at all, since he can start charging after it as soon as it starts repositioning. While charging he can turn, change direction,and hop, and when he actually catches up he can hit a pretty wide area by jumping + thrusting toward it.
That said, as a bow user, you also shouldn't be that far away, which might be part of it. You should mostly be very up close, dashing constantly and cycling through your Charged Shots—really barely out of melee range most of the time. If you're actually running away when the monster focuses on you, that could definitely be contributing.
