So then the OP is a LGPL header-only library, which is always statically compiled in every source. Do we need to do the same thing, and if yes, how we provide an application to allow recompiling?
If you can't use the object files to rebuild another version of the program with a modifier version of the library then no that probably wouldn't be compliant. In that case you would probably have to modify the library so it's not inlining every function. (Disclaimer: IANAL)