The LAN-Only mode is only used when the indoor station (smart device) should not connect to the Internet to reduce possible costs (data usage) (because the outdoor station itself always needs access to the cloud).
If and how the app is connected can be seen by the small symbol (house = LAN, cloud = cloud) right next to the bars showing the signal strength.
The LAN mode also only works for up to 2 direct accesses at the same time - from 3 on the following users/devices are automatically connected via the cloud. If everything is connected in the same network and at least the outstation is connected to the Internet, the connection should work.