You can certainly use automations to control one device based on the values from another.
As the documentation states, the datastream on the receiving device needs to be configured correctly on the device that’s being controlled. This is done in the Automations tab of the template, and the device needs to have the “action” switch turned on for it to be available when you are configuring the automation on the mobile device.
I don’t believe that there is a way to send sensor data from one device to another so that it can be displayed on an LCD though.
If your sending device is something like a NodeMCU or ESP32 then you can use the HTTP(S) API to make your own bridge within your sketch. There are some coding examples in this topic, from this point onwards…
I think that there may now be limits to how often HTTP(S) calls can be made, or how many can be made in a 24 hour period, but you’d need to experiment with that.
Pete.