1) why I need to control the high voltage??
Because you said:
2- I have 2 sources of electricity connected to the arduino : governmental and the generator (but I don’t know how to connect them).I need when the governmental electricity goes off the higher 2 currents shown on the LCD goes off and keep the 3rd and after discussion turn the generator on and keep the 3rd device on, and in case the governmental electricity came give it the priority.
You turn off an appliance by removing it's power.
If you don't need to turn the off and back on to prevent tripping the breakers when the power comes back on, simply ignore my comments on that.
I want to measure current for each device and display current from the lcd ways:
This is a very complicated answer. It is best you understand the methods and calculations involved in doing this, and the site you already mentioned http://openenergymonitor.org/emon/buildingblocks/how-to-build-an-arduino-energy-monitor-measuring-current-only
has a good example of how this works.
Or, If you have already done this and only need to display it on the LCD, there are thousands of examples of how to send data to an LCD. There's even an LCD library on the Arduino playground that you can use.
2)there is not any relay connect
government to arduino and the arduino to generato???
You mentioned that you wanted to use a generator to power the appliances when the government power was removed. To do this, you need a contactor that will keep the two power providers separate. If you do not want to do this, what is the generator for?
3)you did not say how I can control from lcd.
i want to turn off ref. and washer from lcd.
An LCD cannot control anything. It is a display device that displays things you send to it. If you want to control something, it should be controlled from the arduino.