The lye won't dissolve in the solvent as such, but tiny bits may be *suspended* in there, and so end up in your end product.
The fix is easy, just water wash your solvent before the freeze precipitation stage so the lye gets dissolved in the water.
I just squirt my solvent into a measuring cylinder with a few cms of water in the bottom, then pipette it off into my precipitation dish after it settles again.
Make sure the water isn't too cold, otherwise some of the end product might crash out into the water, use water at least as warm as your solvent. Even if you do get cloudy water after, you can just add it back to your soup for recovery on the next pull.