I want to use an LGPL-licensed library in my app for Microsoft's app marketplace. Is that OK?
Here is an encompassing answer:
In short: yes you can. But one important thing to take care of is that the GNU LGPL covered library is dynamically linked, not statically mixed with the main application.
It should also be possible to exchange that dynamically linked library for an independently compiled build. Otherwise you have likely intertwined the library and main application code.
This article may help.
I suspect that because LGPL allows making the source code (of the library that you linked to) available via a download, it must be OK to use an LGPL-licensed lib in your app for Microsoft's marketplace.
Quote from LGPL version 2.1:
If distribution of object code is made by offering access to copy from a designated place, then offering equivalent access to copy the source code from the same place satisfies the requirement to distribute the source code, even though third parties are not compelled to copy the source along with the object code.
The only thing that seems to be an issue is the "same place" requirement, which you will not be fulfilling if your app is being distributed via the marketplace.