Here is one way to do it.
Note that you would replace the "4pcs LED" with another 470 ohm resistor and a solid state relay. The solid state relay can then turn your mains powered lights on and off.
You will probably want to use something other than a battery, I would recommend a plug pack rated at between 9 and 12 volts. (for more than 10V increase the 470 ohm resistors to 680 ohms.)
This circuit has hysteresis, so it has to be quite a bit darker to turn the lights ON than it has to be to turn them off again. This prevents the lights turning on and off repeatedly when the light is dim.
Also ensure that light from the bulb cannot reach the LDR or the circuit will turn itself on and off continually during periods of darkness.