No, you do not have to provide any project files, even when everything is linked statically.
Static linking can be split into two linking steps, first everything except the LGPL libraries can be linked into a big ELF object file, which no longer contains any information about the internal structure and the internal symbols, exactly like an executable file. The only difference between such an object file and an executable is that it contains unresolved external references, like a dynamically-linked executable.
Then in the second and final linking step, the big binary object file is linked with the LGPL libraries.
For compliance with LGPL it is enough to offer access to the big binary object file for the users who would want to replace the LGPL libraries.