You're probably curious as to why I would recommend using distilled water. The soap making process works best with water that is soft and doesn't contain excess minerals or other impurities.
If you have soft water or have access to some, use it! For years I used the soft well water from my Mother's house. I just put it through a Britta filter and it worked great. Now I live too far away and must purchase the water from the pharmacy since our water is quite hard.
You can tell that your water is soft if you feel like the soap doesn't rinse off when you wash. Soft water also requires very little detergent to get your dishes or laundry clean.
Want something a little bit different? Try using coconut milk, goats milk, butter milk or ewes milk to replace a portion of the water.
Add the lye to the reduced amount of water and cool to about 90 degrees F. or 32 degrees C. Incorporate the warmed milk after the lye solution and oils have been combined. Maintain a vigorous stirring with the whisk to prevent clumping in the mixture.
Many other liquids can be used in place of water as well. Tea, beer, wine, coffee, juice, fruit or vegetable puree and aloe vera juice are some of the liquids used. Take note that all carbonated liquids must be flat and all hot liquids should be chilled before use.