Note: I'm not a license expert. The following answer is based on general knowledge of the GPL and LGPL and the LGPL text as found here.
The section of the license provided in the question refers to works that don't contain derivatives of the LGPL library. For example, if I made a sorting library and you made an application for creating lists by reading file contents, your application could be designed to work with my library (create lists such that they are compatible with my sorting library). I believe, in this case, the given section would apply, as you don't have to make any alterations to my library or write any code that derives from it. Your application only needs to be linked to my library.
As specified in Section 0 of the LGPL (emphasis mine):
An “Application” is any work that makes use of an interface provided by the Library, but which is not otherwise based on the Library. Defining a subclass of a class defined by the Library is deemed a mode of using an interface provided by the Library.
A “Combined Work” is a work produced by combining or linking an Application with the Library. The particular version of the Library with which the Combined Work was made is also called the “Linked Version”.
Thus your library, by extending
PHPMailer, is an Application that uses the library.
In Section 4, we see that you are allowed to share your library under any terms, as long as they do not restrict downstream users from using the original library under the terms of the LGPL.
You may convey a Combined Work under terms of your choice that, taken together, effectively do not restrict modification of the portions of the Library contained in the Combined Work [...]
In other words, your library can be available under whatever terms you like, as long as the LGPL library is still available under the same terms determined by its original author.