Realistic answer: This sounds like the worst way to hunt a large animal. Lances can only be used effectively once, when you charge the beast, and it will likely maul you before it dies, which it might not.
Awesome answer: This sounds like the BEST WAY to hunt an enormous dinosaur! Lances are for cavalry charges, which is a wicked cool way to fight a huge terrible lizard!
The dinosaur has a long reach, so you need a longer spear. It could be so front-heavy that you'd need a support on the saddle in front of you, a support on another horse in front of you (which defeats the purpose of having a long spear, but hey! Teamwork!), or you need to hold the lance upright as you charge and drop it at just the right time so it's level with your target at the moment of impact. Or just be super strong. That works too.
It should be made of a material with a high strength per volume ratio (specific strength). It needs to be strong but thin so that it punctures well. Titanium ought to do the trick, but there are some other materials with even higher specific strengths that have really great names like Zylon, Vectran, and of course "colossal carbon tube" (see Wikipedia page on specific strength). What are these? How are they made? What do they look like? I have no clue, but the names are sweet and they have Wikipedia entries so you can read up on them.
Aaanndd... the Gruesome Answer: Blood loss and trauma are key to surviving the fight. Unless you are lucky enough to sever critical nerves with your first strike, your beast will not go down fast enough to keep it from wrecking you. Unless you can make it bleed faster.
Here's what I have in mind: a telescoping spear that collapses on impact, but as it collapses blades pop out from all sides of it, shredding the innards of the target. This weapon would have huge stopping power because it would scrape through the target rather than sliding. Your knight would probably be thrown from his horse as the lance absorbs all of his momentum. (I also assume that the dinosaur is charging at your knight, so double trouble.)
This lance - let's call it the Death Flower - could also help a knight that has fallen from his mount: if he is charged by a foe, he can plant the butt of his Death Flower in the ground and aim. The terrible lizard hits the spear and comes to a halt inches away from the knight because all of its forward momentum has now gone into liquifying its own internal organs. Brutal.
Again, this is a one-shot weapon. Maybe bring spares.