By the way, protein is 4.3 calories per gram, and that 40 gram maximum I gave you is quite high and for a very large child.
About that lactose-free milk and uncertainty with cheese... Lactose is a baby sugar and babies are designed to digest it. Except for incredibly rare cases, all babies can "tolerate" lactose, when they are healthy. When a child's digestive system is upset by sensitivity reactions to foods, such as milk proteins or soy proteins, they will temporarily stop making adequate lactase enzyme and thus have problems digesting lactose. Other things that will reduce lactase enzyme availability are diarrhea of any cause, and antibiotic use. So, a child who reacts to milk may do somewhat better on lactose-free milk, but they will not be entirely free of symptoms. In almost all cases, it's the milk proteins that are problematic for babies and young children (as well as a large number of adults, though lactose intolerance is common in teens and adults as well). In cheese, the proteins are partially pre-digested by the bacteria that make the milk into cheese. Different kinds of cheeses will have more or less intact milk protein. This is the likely reason you are unsure about cheeses. I recommend your child receive NO milk, cheese, dairy yogurt, cream, whey, casein, or other milk ingredient. Even butter has small traces of protein in it; enough to keep many a child sensitized. Watch out for things like "non-dairy cheese" or "non-dairy whipped topping." Strangely, these products are generally filled with milk proteins. For marketing reasons, the term "dairy" seems to only mean lactose. Any vegan product should be entirely milk-free, and if a product says "no milk," that should be OK. You need to read ingredients.
Goat and other common animal milk proteins are very similar to cow proteins and most (but not all) who are sensitive to cow's milk proteins will eventually develop sensitivities to other milks. Unfortunately, raw milks have the same proteins (and no, they don't digest themselves unless you're talking a little protein and lactose digestion in very soured milk). In studies, as well as in people I've worked with, these are shown to be just as allergenic for most of those who are already reactive.