Assuming your PC is a medium sized one, by RAW, No, you can't,
From SRD,
If your mount charges, you also take the AC penalty associated with a charge. If you make an attack at the end of the charge, you receive the bonus gained from the charge. When charging on horseback, you deal double damage with a lance (see Charge).
So, that is the mount who charges, not the rider. The rider just get the benefit and penalty of charging. And the mount must follow the rule for "Movement During a Charge".
From SRD,
Movement During a Charge: ...... First, you must move to the closest space from which you can attack the opponent.
You and your mount shares the same space, and a huge dragon has 15 foot reach. Thus it stops at that distance (15 foot to the foe). Now, monkeygrip feat does not change the reach of the lance. So, if you are a medium-sized creature, your lance's reach is still 10 foot. So you cannot "make an attack at the end of the charge".
The reach of the mount's longest attack and the reach of the rider's weapon must be the same.
It is funny that strictly by the rules as written, usual horse rider cannot make a lance charge
Ride by Attack feat does not help. First of all, the feat's description is broken. By the combat rule, the rider does not move by himself nor take charge action by himself. The mount does. And, even if we ignore that mistake, the feat's benefit is "you may move and attack as if with a standard charge and then move again". So, it just allows you to move AFTER the charge is solved. The initial procedure of charging does not change at all.
Of course, mounted charge rule in PHB is a rather silly rule flaw. And many playgroups are ignoring it and using some kind of house rules.
#Edit
If you are actually a large rider with 10 foot natural reach, you can attack at 15-20 with your lance. So, when the huge dragon stops at the point 15 foot to the enemy, you can use your lance.