I am not a lawyer, but I have spent a good deal of time dealing with similar license and distribution issues relating to software. My advice is not legal advice and you should not depend on it.
I gave the FIPL a close reading. It offers terms similar to the LGPL2.1, with some additional conditions.
Here's a brief summary of the license terms.
(1) You can use the library with your closed-source application to produce a distributable work without having the library's license term extend to the entire work. The combined work can be distributed under any license you choose.
(2) You can only redistribute the library source code under the FIPL, if you choose to (or are required to, see below) distribute it.
(3) If you make any change at all to the library source code, you are required to make the sources available under the terms of the FIPL. That applies only to the library itself, not the combined work, although your application must provide a way to communicate that a modified version is available and how to obtain it (ie. some lines in a dialog box or something).
(4) Mr. Floris van den Berg reserves the right to arbitrarily change the license terms at any time but not without changing the version number, so you should explicitly specify the version of the license you are using.