Is this situation required to release the entire source code of our app under the LGPL 2.1 (or LGPL 3.0) license?
No, that's not a requirement of the LGPL license.
But if the developers (wrongly) believe that it is a requirement of their license (even if it's not), they may take down your app (and maybe even your developer account) with a simple copyright notice. So it's not worth the headache.
Topic:
Code Signing
SubTopic:
General
Tags: