Recoil is a matter of momentum. Damage to the target is a matter of energy. The two are not the same thing, and it is perfectly possible for one weapon to deliver a greater energy with less recoil than another. I’m 100% certain that the lance would deliver significantly more momentum than any handheld firearm, but I’m not sure about the energy offhand.
Back to the OP, a very lucky human could hit a vulnerable spot and kill the dino (and it’d have to be luck, not skill, because a rex’s vulnerable spots wouldn’t be in the same places the knight would expect), but my money’s still on the pit trap or poison.
The tendons at the back of the legs are probably the most practically-accessible vulnerable spot, but one additional complication with that: The intended effect of a good, solid axe hit there is to make the dino fall over, but it’s probably going to fall over towards the injured side. Which is likely to be right on top of our stalwart axeman. And even without teeth or talons, an animal that big falling over on top of you is likely to be fatal in itself.