I2C is a bus, it is designed to have multiple slaves. Connecting the RTC and the LCD should not be an issue.
I still don't understand your power switching and in particular how you are powering the Arduino which powers your other components.
You are doing some kind of power switchover and then all you said about the arduino is:
The arduino is powered with an independentment transformer.
This doesn't say where that transformer is getting its power and whether that power is also being switched.
It sounds like you may have some large power transients during these switch overs particularly if you have large loads that are on while the switchover occurs.
That can create create issues for power supply feeding the Arduino which in turn can cause issues for the components powered by the Arduino.
Can you provide a better more detailed description of the power and how the power is being cut-over and what types of devices are on during this cutover.
--- bill