The first thing I'd try is changing butters - but that isn't going to make a difference because the inherent problem is with the cooling down of the lip balms, and every butter will go grainy if it isn't cooled properly.
Butters have different fatty acids with different solidification points. If we make lip balm (or other creations with butters) and leave it on the counter to solidify, the butter will go through those temperatures slowly, which can cause grains. If we put the creation in the fridge or freezer, they will cool down more quickly, which doesn't give the fatty acids a chance to crystallize, and we shouldn't get grains.
Some of us are cursed with graininess: There isn't an easy way to tell which of us will be plagued with little gritty bits in our lip balms and which won't. But a quick cool down of your lip balms, lotion bars, and other anhydrous creations like sugar scrubs or whipped butter should ensure fewer grains and more butter-y goodness.