There is almost certainly no need to use an interrupt to read the switch as has been pointed out. The loop() function should repeat fast enough to read the input and allow a response in a short time.
It sounds like your program has 2 display modes, LDR mode and LED mode. Declare a boolean variable, lets call it ldrMode. When it is true, which will be most of the time, display the LDR value, but only if it changes. When the button becomes pressed, detected in loop(), set ldrMode to false, save the millis() value, change the LED mode and display the appropriate message. Each time through loop() check whether millis() minus the start time is equal to or greater than the required period. If it is then change ldrMode to true and display the LDR value. If not then keep going round loop() until the period ends.