Could we make armor that would protect you from a direct hit by a lance wielded by a horseman riding at full speed? I imagine even if it didn't pierce the impact would still rupture multiple internal organs.
It's called a armored vehicle.
Alternatively it could involve wrapping someone in like 10 ft of mattresses.
That said against an object that large and that slow hitting you you really only have three options of defense.
1) Form some sort of immovable wall in front of you, this is basically what a pike defense did, since you would brace the pikes against the ground to transfer the impact downwards instead of into the carrier.
2) Wrap whatever you want to defend in enough padding to dissipate the force. For most things this would require way too much padding to feasible.
3) Make something that rolls with the impact to dissipate it. If you were surrounded by a well-built rollcage then it doesn't matter how hard the horsemen hits you, since you would just go flying backwards until you ran out of force.
As you can see, really the only feasible option is the pike style option for a personal defense level.
Probably not. The horseman would probably have a similar impact to a bullet, since he'd have a much higher mass even though he's moving more slowly. There's also the problem where it's entirely possible you'd be hurled backwards, depending on the weight of the warhorse and the skill of the lancer.
Actually I think you'll find the charging horse has a lot more impact energy than a bullet, simply because it outweighs the bullet mass by such a huge amount. Making some general assumptions based of the data I could find for the 5.56x45mm NATO rounds and the average medieval warhorse + knight, even if the warhorse only successfully imparted 1/10th of it's energy on impact, your bullet would need to be traveling at
Mach 600 (about 18x faster than Earth escape velocity) to match it in energy imparted (assuming the bullet hit the target and stopped dead), which is approximately 220x faster than their actual speed.
Weight of a 5.56x45mm NATO round: 4.1 grams
Speed of the round: 940 m/s (Actually the 4.1 g ones only go at 905 m/s * 936, but I erred on the side of the bullet)
Weight of a warhorse: 2000 lbs (Some could go up to 2200 or so lbs)
Weight of Knight + equipment 230 lbs (figure 180 for the knight, 30 for the armor, 20 more for other things)
Warhorse charging speed: 30 km/h = 8.333 m/s (Some horses can obviously gallop much faster, but I dropped it to account for breed and weight carried)
Force of the Horse+Knight = 8.333 m/s * 2230 lbs / 2.2 (lbs/kg) * .1 (impact factor) = 844.663 N
Force of the round = 940 m/s * 4.1 g / 1000 (g/kg) = 3.854 N
Ratio = 844.663 N / 3.854 N = 219.165
Speed of sound reference (in air) = 343 m/s