You can statically link Qt in compliance with the LGPL. The LGPL only requires that users are able to substitute the LGPL'd portion of an application with an alternative and compatible implementation.
Using a shared object/DLL is the traditional way of doing so, but you can also accomplish this by providing the object files for your application to allow users to link their own substitutions statically.
The FSF explicitly permits this as documented here:
Using a shared object/DLL is the traditional way of doing so, but you can also accomplish this by providing the object files for your application to allow users to link their own substitutions statically.
The FSF explicitly permits this as documented here:
https://www.gnu.org/licenses/gpl-faq.en.html#LGPLStaticVsDyn...