Because Eagle projects are self-contained including all the data related to parts used in them (rather than just referencing a library at run-time) it's possible to extract a part from a project even if you don't have the library that was used to create it.
Open the project in Eagle, go into the board layout (not the schematic), and from the menu select "File -> Run...". You'll see a huge list of included scripts that can be executed. Find the script called "exp-project-lbr.ulp" and run it. You'll see a screen that gives you some options about generating a new library using the parts found in that project. Click the "Collect data" button to make it populate its list from the project, then "Create library" to actually save it.
You'll now have a library containing just the parts that were in that project, and can use it in your other projects.
Note that this is a technical solution, and I haven't mentioned anything about the legality of it. If the original library was for restricted use it's possible you're not allowed to use it in this way, but I expect that anything created specifically for the Lilypad was likely to be under some open licence anyway.
Power-over-Ethernet injector: http://www.freetronics.com/poe-injector-4ch