The long sword has the same initiative when compared to a lance, actually, and a mounted knight usually carry both weapons. Why would he use his lance?
I would suggest something along these lines:
Lance: When using this weapon in a mounted charge, use the Strength of the horse instead of the Strength of the rider when calculating the Damage Total. In addition, if the optional rule for Evasion is used, the target can only use his Evasion Total to defend himself, not his Defense Total.
Long Spear: When using this weapon to interrupt a charging attacker, a character who is wielding a long spear has a +3 bonus to his Action Priority Total.
Eirik