A standalone executable that dynamically links to a library through a .so, .dll, or similar medium is generally accepted as not being a derivative work as defined by the LGPL. It would fall under the definition of a "work that uses the Library". Paragraph 5 of the LGPL version 2.1 states:
A program that contains no derivative of any portion of the Library, but is designed to work with the Library by being compiled or linked with it, is called a "work that uses the Library". Such a work, in isolation, is not a derivative work of the Library, and therefore falls outside the scope of this License.
Essentially, if it is a "work that uses the library", then it must be possible for the software to be linked with a newer version of the LGPL-covered program. The most commonly used method for doing so is to use "a suitable shared library mechanism for linking". Alternatively, a statically linked library is allowed if either source code or linkable object files are provided.
Does that mean I can statically compile LGPL-covered libraries with a proprietary application? I just don't know English that well to clearly understand what exactly that text means.
Btw, russian version of that article says that some proprietary programs are linked with LGPL-covered libraries statically because LGPL doesn't restrict static linking with non-free programs in any clear way.
A standalone executable that dynamically links to a library through a .so, .dll, or similar medium is generally accepted as not being a derivative work as defined by the LGPL.
So a dynamically linked library is generally accepted as not violating the license.
Essentially, if it is a "work that uses the library", then it must be possible for the software to be linked with a newer version of the LGPL-covered program. The most commonly used method for doing so is to use "a suitable shared library mechanism for linking". Alternatively, a statically linked library is allowed if either source code or linkable object files are provided.
Using a newer version isn't trivially possible, unless you also provide all the components needed to recreate it (possibly with a newer version), so having a statically linked version of those libraries means you have to provide things you don't with the dynamically linked versions.
So yes, this does say that you're allowed to ship binaries that have those libraries statically linked if you also provide the user/downloader with a way to recreate it.