I've generally stopped using lip balm, and just apply the sunscreen to my lips. Minimally noticeable taste with some; none with others. I may be running somewhat more of a risk with becoming sensitized and developing an allergy to the ingredients, but so far, so good.
Bottom line is, the lips are a frequent site for the various skin cancers to show up; protection there with sun-screen is better than the the lip balm that you don't have. It's also one less thing to buy/pack/carry.