What the LGPL requires is that the end user be able to take the source code for the LGPL part, modify it, recompile it, and then replace the functionality in your binary provided by that part with their new part.
Obviously with dynamic linking this is almist trivial, the end user replaces the so or DLL and done.
With normal static linking, it's only a bit harder. If you ship alongside your binary a bundle of eg .o files and a script that links them together with a .a for the LGPL part for example, this is also compliant without revealing the source code to your non-lgpl part.