If you use deionized water alone the pH will not change - just dilute sludge with more water, no? You can measure this with a pH pen. Demineralized water is at pH 7.0 but has no buffering capacity, and so pH will not change when added to a solution at pH 2.0 or 13.5 - no need to add lye I would say, water alone will dilute the sludge. If a pH of 13.5 is the target for an STB, and if you measure it, you'll find that one needs very little lye to hold the pH at this scortching high alkaline value...