How is it not fair that 1h cav can use lances, too? Like historical knights.
Anyway the slots isn't the problem at all as cav shields are 1 slot but the dropping is, a mixed lancer often has to play that way already, use lance, use sword, ride back to pick up the lance again.
And I have to say I actually like the idea, if you spawned one of the weapon racks at spawn lancers could kill someone and ride back to their spawn to get a fresh one (lance should only break if you killed someone though and maybe made cheaper/stronger). I don't see a big problem having to run back to spawn (or switch to sidearm, spear, morningstar or 1h) after making a kill.