Of course, the best thing to do is only buy organic. But I've soaked both organic and non-organic nuts exactly this way, and the stuff that comes out of the non-organic nuts is really gross. I took a picture of the non-organic nut soaking water below to show you.
Now, before you start saying, "That's just the lemon juice making it that color" let me tell you: It isn't. :-) First of all, I only use about 3 tablespoons of lemon juice per gallon or so of water, which isn't nearly enough to cause this color. And secondly, this liquid isn't only yellow, it's opaque. You can't see through it at all. That's disgusting.
After I dispose of the filthy water, I soak the nuts for another few hours in fresh water. When the time is up, I strain and rinse one more time before dehydrating them in my Nesco dehydrator. My advice: Buy organic nuts. But if, once in a while, you don't buy organic, try my technique.