No, you should not if you're seeing signs of runny stools!
Just like humans, cats can be lactose intolerant. While some cats seem to handle milk fairly well, many get diarrhea from it. Some cats may also get an upset stomach, or it may even trigger vomiting.
From the WebMD article:
Most of us have probably given our cats a bit of milk and never noticed a problem. That’s because some cats tolerate milk just fine, Wynn tells WebMD.
How can you tell? Try offering your cat a tablespoon or two of milk. If you don’t see symptoms within a day, chances are good your cat will do fine with milk as an occasional treat.
Still, most veterinarians don't recommend it. Cats don’t need milk, and the potential problems outweigh the potential benefits.
Remember that treats of all sorts -- such as tuna, meat, cheese, or other “people foods” -- should make up no more than 5% to 10% of your cat’s diet. The rest of your cat's calories should come from a high-quality, nutritionally complete cat food.
Note that some cats apparently do not have a problem digesting milk, even as an adult. There is speculation that this may be an evolutionary response to the domestic relationship between cats and humans, due to human cultivation of cows as a food source:
However, early during the domestication of sheep, cattle, and goats, humans appreciated the milk of these animals as an extremely valuable food resource. Interestingly, as humans began using dairy products in their diet, nature selected for those individuals in whom production of lactase persisted into adulthood, which gave them an advantage over those who could not digest lactose but instead became ill from consuming milk. Lactase Persistence is a gene. Those individuals in whom the gene expressed itself were healthier and longer-lived due to the superior nutrition received from milk. They were more likely to have more children, and so the lactase persisting gene got passed on and spread. Lactase persistence is most prevalent in people of European descent, because very early in this period, cattle spread with humans from the “Fertile Crescent” into Europe with the Neolithic Expansion. The gene mutation, enabling Lactase production into adulthood, originally occurred in the region of today’s Austria and Hungry, and began spreading 7500 years ago from there throughout Europe – especially northern Europe.
By nature, cats are attracted to foods rich in protein and fat from animal source. 9000 years ago, milk and simple dairy products would have caught their attention as much as these foods do today. Thousands of years ago, people most likely delighted in gaining an animal’s affection by offering it food in the same way as we do today. By which other way could domestication have occurred? Cats may have been exposed to milk and dairy product as food past their infancy for nearly as long as people have. The possibility exists, that some cats have developed Lactase Persistence in a similar way that people have. In fact, there are some strong hints made among those who study evolution, that domestic cats , especially from European descent, have. Such a suggestion was re-published, for example, by Jerry A. Coyne, Ph.D, Professor in the Department of Ecology and Evolution at the University of Chicago in an entry in his blog.