I don't have LiOH, but I have a 1 Kg canister of K2CO3 and one of KOH. However from past experience I think that by increasing water conductivity the spark discharges will be much weaker. In any case, I kept testing and I don't know if it still is a coincidence, but I'm getting increasing Geiger counter readings.
For the record after each run I am taking the consumable electrode out of the solution and putting it aside on a plastic support. Initially I did this in order to let the cooling fans run to remove some heat from the cell and not have to electrically disconnect the anode, but I'm wondering if this is having an effect. (EDIT: see photo; the electrode is resting on the lower right corner)
Another possibly coincidental happening is that counts started increasing after I refilled more distilled water, since it was evaporating out too quickly. Below I put a screenshot of a 127 CPM peak, but I just got one at 129 CPM, by the way.