mtomovich:
I can't really get a clear view on what exactly I'd need to release to the public (if anything) to comply with the LGPL license.
Which indicates that you have not read the actual license...
https://www.gnu.org/licenses/old-licenses/lgpl-2.1-standalone.html
Section 4 is quite clear that you have to provide object code or source code for the libraries you use. My guess is that you can provide a reference to what you used (I don't understand the second paragraph).
To be more specific, I'm not redistributing software or anything...
Really? The AVR processor in your product is blank from the factory? Is such a product very marketable? If your product really does not include software, why are you concerned about the LGPL?
Do I still have to release object files?
See Section 4. For the libraries you use, yes (or source code).
Looks like it to me (see Section 5)...
However, linking a "work that uses the Library" with the Library creates an executable that is a derivative of the Library (because it contains portions of the Library), rather than a "work that uses the library". The executable is therefore covered by this License. Section 6 states terms for distribution of such executables.