Bubbles Galore said:No it won't weaken the strength of the lye.
If you're using goat milk slushie, adding just a bit of lye will melt the iced milk quite quickly. You can sit your jug of milk in iced water to keep it cooler and stop the milk from scalding.
I prefer to use goat's milk frozen into ice cubes. I add the sodium hydroxide (lye) bit by bit and the result is always a nice, pale colour. The temperature never gets too high and the soap is always fantastic.