There has always been a lot of confusion and FUD around this issue.
First off, libmysqlclient is GPL 2, not LGPL, (which would argueable be more in line with it being a library). However, there is a so-called FLOSS exception in effect, which allows free and open source projects to use and distribute libmysqlclient without having to adopt the GPL license.
In your case, I think you may only link to (and/or distribute) libmysqlclient if your application is also GPL, or goes by another open source license (as per the FLOSS exception)
