Communication between the car and the charger is different from communication between the car and the phone app.
We do not have wall chargers for our Teslas but just use the factory-supplied portable cable plugged into a NEMA 14-50 plug. All the charging information is available on the phone app, as the information is communicated from the car through the LTE connection, not through the charger. I expect it will be the same with the Lucid.
Does the phone need to be connected for the schedule to take place?