If you have the dual wielder feat, and you are riding a mount can you wield two lances. Also what would the damage dice be?
Yes, you can.
Also, a lance requires two hands to wield when you aren’t mounted.
So as long as you are mounted, you can use a lance in one hand. The Dual Wielder feat allows you to use two-weapon fighting with any one-handed melee weapon, so this works fine.
As for the damage die, the damage die for the lance is a d12, and there's nothing in its special property or in the dual-wielding rules that would change this.
If you were riding a standard horse, as a DM I might have some qualms about you using dual lances. But a paladin with his own Find Steeed horse could telepathically control its movements, therefore I would allow it.
Impossible fighting style. I would never allow it even if RAW, it's surely not RAI. Two reasons; first, you need a hand to steer your horse, second, physics. Lances damage comes from impacting a big mass (you and the horse) into a small area (tip of the lance). If you double the area you get ideally two times half of the damage and thereby loose control of your mount so it's absolutely stupid to do so and without any advantage.