Where to put the Flyback Diode in a Relay Module?
There is undoubtedly already a catch diode in that module, so adding one won't help one bit. 

You should get a module with opto-isolation and supply the relay coil power from a separate power source with no connection to the Arduino power.  

Also keep the wires to the contacts well away from the wires to the LCD module. 



You should, however, connect a diode across the solenoid (assuming it is a DC type!) so that it is reverse biased. 

If it is an AC type then there is not much that can be done. An RC snubber will help a bit, as will a MOV or TVS but they are not greatly effective in reducing this kind of electrical noise and things will only get worse as the contacts wear.