>If you're really stumped, draw a map. The game's geography appears properly Euclidean, though many passages "twist" (in the sense that one room's east exit would tie to, say, another room's north exit, rather than its west exit).

I made a large flowchart for all of the locations. It's every single area I can access. What have I found? I killed a guard, a sand monster, and a dragon. I dipped my lance in the river just because the option was there. An old man wants a piece of parchment I don't have, and there's a goblin who is immune to my efforts.

Nobody who wants a lance, or would have any use for one.

Is the lance-owner supposed to be in the castle, or something? I've been outside of that place for a while.