I don't know if it can be disassembled, but you can buy siliconspray with a very narrow extension. Just push the extension in the inside of your puzzle and spray a little. It is a bit messy, but I was able to lube my 2x2x2 this way.
I think having the puzzle disasembled is better for lubing, you get a more even coat.
To disasemble your square one, turn it verticaly 45?, then turn the U slice and two edges should pop out. From there it's easy. Reasembling is alittle harder, but just remember to put in all 8 corners before putting edges in.
I don't know if it is very wise to disassemble the square-1. It can cause that the Square one will become looser and looser and finally break in two halves.