The problem is that you have two hosts with the same name "BGW" (= "BGW.local" MDNS name) in the same network. They should have different names.
Is this a known limitation of LwIP’s mDNS implementation? I haven’t done an audit, but from my experience with mDNS, the “Probing” step of claiming records should ensure the hostname is unique. See
https://tools.ietf.org/html/rfc6762#section-8
I've worked with Apple’s mDNSResponder and if two devices have the same hostname, the one that detects the collision ends up adding “(2)" the hostname to make it unique.
Joel