The aim of the research was to evaluate lactose content and rheological, physical, chemical, and organoleptic parameters during the storage of fermented beverages made from sheep’s milk. The research was carried out on natural, probiotic, and Greek-type yogurts, as well as kefir. The products were made using the thermostat method from the milk of 42 East Frisian sheep in the middle lactation period, in duplicate. Lactose contents, active and titratable acidity, color by the L*a*b*C*h* system, and rheological parameters (hardness, consistency, consistency, and viscosity) were tested, and organoleptic assessments were carried out on the first, seventh, fourteenth, and twenty-first days of storing the drinks at 4 °C. Of all drinks, the highest reduction in lactose after 21 days of storage was found to occur in kefir (52% reduction) and, among the yogurts, in the Greek yogurt (41% reduction). The product with the lowest lactose content, regardless of the storage period, was kefir. This indicates that kefir is more suitable than yogurt for people with partial lactose intolerance. Effects of both inoculation type and beverage storage time were shown to exist for all parameters. It was also found that kefirs suffered deterioration in most rheological parameters and, in general organoleptic evaluation in the final period of storage. Based on our analysis, the optimal storage time for natural yogurts and sheep’s milk kefirs at 4 °C was 21 and 14 days, respectively.