Continuing the investigation:

It appears as though Poser creates a web server on the localhost on port 11530.  That server root directory appears to be Runtime/ui/Flex/serverRoot/

If I open that directory in the finder, all I see is a nonVirtualAssets folder and a crossdomain.xml file.  It looks as though there should be an assets folder in here, too, yes?  Yet, despite its absense, I can still see http://127.0.0.1:11530/assets/addLibraryButton.png

A Spotlight search on my entire drive for addLibraryButton.png yields nothing.

Running LSMGUI.html in Safari without Poser running indicates that the Flex is looking for a Python script:  http://127.0.0.1:11530/apps/lms/api.py

Upgraded Python to 3.2.1, just in case Lion's pre-packaged version is incompatible.  No dice.

Tried this:  downloaded the addLibraryButton.png graphic, created a folder in serverRoot called "assets," and dropped it in.  Ran Poser.  The icon didn't show up, but it didn't show its "broken link" placeholder, either... it's just missing.

Uh-oh: after upgrading Python, my Runtime no longer shows up in the Lbirary tab... just "Downloads."  I can still load things from my Favorites tab, tho, so they're still there.  I try using the Search tab and... whoops.  Typing into the Search text box puts two characters in for every keypress (typing Victoria results in VViiccttoorriiaa), and trying to search on that produces the following error:

XML parsing error: 'not well-formed (invalid token)' at line 5

Ugh... what a mess.