Perhaps you are trying to say something else or dont know the right words to use but you have simplified what youve read or how you understand it into this awkward statement.
'Essentially breaks LAN encryption' is not correct / is not a thing.
Airsnitch lets an attacker attach to a wireless network and snoop on other traffic routing though the same access point, including traffic routed through a separate SSID/VLAN/Subnet, previously believed to be isolated. There is no 'LAN encryption' involved here.
The context of this post was a client on a public network, like a hospital.
If said client is just a guest on the open network, and attaches and successfully connects to a VPN, Airsnitch does nothing. Even without Airsnitch, an attacker who is capturing the unencrypted open ssid traffic in the air could do the same thing, capture all packets of this users traffic, and -all- of that VPN traffic would be encrypted. This is why a VPN is the best option when on public networks. Man in the middle is not possible when the traffic is encapsulated, versus raw https, because the traffic is not at all exposed outside of the tunnel.
Airsnitch would be troubling only for the other hospital networks/subnets also broadcasting access alongside the public network. In this case an attacker would potentially be able to access the hospital LANs not intended for public access. However typically access to network file storage and other systems have additional authentication that isnt magically broken just because they can be reached.