It is widely known and accepted that you need to dynamically link to satisfy the LGPL (you can static link if you are willing to provide your object files on request). There is a tl;dr here that isn't bad: https://fossa.com/blog/open-source-software-licenses-101-lgp...
But, speciically the bit in the LGPL that matters, is secton 5: https://www.gnu.org/licenses/old-licenses/lgpl-2.1.en.html#S... - particularily paragraph 2.
As always, IANAL, but I also have worked with a lot of FOSS via lawyers.
Also, this is and always has been the view of upstream FFmpeg. (Source: I work on upstream FFmpeg.)