just make the heavy lance 3 slots like a pike or long spear, since its the same thing but with insta kill couch and usable while mounted, outputting vastly more damage each round than pikes and long spears do.
1hand/shield or 2slot weapon + heavy lance is annoying when you dismount the lancer and they begin poleaxe spam or turtle up and become regular infantry, this will require them to use only a 1 slot weapon, only a shield, or try to scavenge weapons after they get dismounted to become effective infantry again. a simple non intrusive way to discourage 5-6 riding in any melee build instantly becoming a master of all trades every round from spawn on.
ruining athletics for builds with riding is just awful.. athletics is already a luxury for most ranged cav classes, and a pure lancer doesn't use athletics to have higher PS or riding skill already.
I put riding into my 2hand build so I can mount up when I'm sick of infantry and as an internet knight playing an internet horses game it would shatter my immersion to not be able to ride horses without having a gimped useless build for infantry combat. I rarely bring a lance but when I do having a heavy lance + longsword or any other good weapon is just silly. I would glady trade off needing a 1 slot weapon to have the mounted power of a lance.
Just deal with what is easily the most imbalanced part of cavalry, the lances, and making it 3 slots would be a sane nerf.