The weaver gives you three quest for different equipment types. You get the recipe for the Mithril Bucket in one of the other two quest she gives you.
Leneth can be recruited when you interact with the top right icon in the tasks section of the command center screen. It requires that you advanced the events with Jackie and Lexi, that you had sex with Leneth, and that at least one small and one big harpy was captured and released at the big farm. Maybe the part with Jackie and Lexi is missing for you?