The rot can be due to too much moisture and also hotter temperatures. Lily bulbs don't do well when the temps are high and it can be more difficult to keep their "feet" cool in pots. Trying to compensate for either of these with chemicals will not work well. From my experience err on the side of too much drainage - as suggested add more grit or mulched wood. Peat moss in the mix breaks down over the season and your drainage will decrease. Many of the potting mixes are only good for one season and if I am potting anything for more than one season I mix 1/3 with wood chips/mulch to give structure and provide drainage.
