After Grigor the Unhelpful leaves, turn around and look for a small black box on the wall. Use Niobe's key in it to reveal --
-- of course a puzzle, what else? Read to the end of this hint for the settings you need.
At first glance, this looks easy; you just move the black pieces around so the spider has a clear path up. But!
Every time you move the black pieces around, the circles inside the web move too. In order for the spider to get out, the entire path needs to be clear.
Did you see the numbers above and to the right of the web? They're significant.
They're telling you what numbers you need to see on each side of the black pieces in order to let the spider out.
You know, I'm just not a numbers person. Here's the answer:
Spider Puzzle, Amateur
Spider Puzzle, Master
When you've got the path clear, press the red lever at right. Then go off to the ferryman to find what Grigor left you.
How do I get the thing Grigor left for me?