IANAL. Assuming LGPL 2. God help you with version 3.
You do not need to license your code that uses the library as GPL or LGPL, but you need to permit modification of the combined work (meaning your code and the library together) as well as reverse-engineering for debugging such modifications. You still have to honor the other aspects of the LGPL for the library which uses it (not for your code that uses the library).
Section 6 of the LGPL v. 2.0 says,
you may also compile or link a 'work that uses the Library' with the
Library to produce a work containing portions of the Library, and
distribute that work under terms of your choice, provided that the
terms permit modification of the work for the customer's own use and
reverse engineering for debugging such modifications.
I believe that when they say, "modification of the work" they mean the combined "work that uses the library" which means you have to permit modification of the combined work as well as reverse-engineering for debugging such modifications.
The company I work for specifically does not want to permit modification or reverse engineering of their proprietary code, so we do not distribute any LGPL code with our application. Neither will we distribute any GPL code unless it specifies the Classpath/Linking Exception.
The GPL 2 with the Classpath/Linking Exception is similar to the LGPL, except it does not impose those restrictions on a combined work. The last section of that Wikipedia article backs me up on this.
In my mind, the GPL 2 with the Classpath/Linking Exception has roughly the same intention as the Apache 2 license, but the Apache license is much clearer about it. I believe that the GPL 3 is worded to prevent the Classpath/Linking Exception.