Before we try to solve your specific problem, let us “digest” the topic a little more broadly.
There is a rabbinic prohibition to undergo medical treatment on Shabbat.[1] This prohibition was instituted out of concern that one might violate Shabbat in the course of the treatment or, in the classical situation, in preparing medicines (by grinding). However, the breadth of this prohibition is reduced at two, opposite ends. When one is truly sick, he is permitted to take medicine to improve his condition. Also, some health-related actions are too minor to be considered medicinal.
Food, in addition to being tasty and to providing energy for the day’s activities, may also have medicinal value in a variety of ways. Yet, even specifically healthful foods are not included in the prohibition of refuah.[2] Those things, including some herbs and tablets, that are arguably food-like but are normally eaten only when one is ill are prohibited.[3] Does this prohibition pertain also to a person who is well? The Shulchan Aruch[4] says that healthy people are permitted to consume these items because they do not need refuah. Some explain the reason for this halachic distinction as follows. Although one who is ill may be distressed enough to inadvertently violate Shabbat when seeking a remedy, this concern does not apply to a healthy person.[5] On the other hand, the Magen Avraham, one of the Shulchan Aruch’s primary commentators, tries to prove that medications are prohibited even for those who are not suffering at all.[6] The Tzitz Eliezer[7] and Rav Ovadya Yosef[8] accept the Shulchan Aruch’s opinion, but Rav Moshe Feinstein[9] says that it is difficult to dismiss the Magen Avraham under normal circumstances.[10]
An apparent, common application of this machloket concerns whether a healthy person can take vitamins, which are not really food (we don’t make a beracha on them). However, Rav Feinstein rules that it is permitted to take vitamins on Shabbat, even according to the Magen Avraham. He reasons that a medicine must make some type of improvement to the body. If a compound just helps prevent disease by providing the body with substances that keep it working smoothly, then it cannot be considered medicine.
What about lactase pills? There are different ways to look at the matter. On one hand, the person feels fine when he takes it. On the other hand, he has an existing deficiency which will, given that he ingests milk, cause him discomfort in the relatively short term without the pills.[11]
Fortunately, when it comes to lactase pills, there are additional grounds for leniency, based on how they work. Most medicines strengthen the body or fix problems that have arisen in it. Interestingly, lactase replacement pills act differently than most pills. They provide the enzyme without which the consequences of lactose intolerance follow. They simply break down milk’s lactose into sugars that the body can absorb. In fact, the active enzyme can be added directly to the milk, and the desired breakdown will occur outside the body. Thus, the pill just causes that the problematic condition never arises. The body’s deficiency is not addressed, as it is not healed into producing its own lactase enzyme. Therefore, the situation is more lenient than even that of vitamins, which help give the body strength and resources to deal with future problems.