Unfortunately FAudio cannot, counterintuitively, link to LGPL code, because it needs to be able to run on embedded platforms, which (for reasons I do not understand) cannot ship any LGPL code.
It's quite simple. If a platform (such as Nintendo Switch) does not allow users to sideload their own code on it, it's not possible to comply with the terms of the LGPL while shipping LGPL code on that platform, because the user cannot install their own modified version of the LGPL library.