I'm lactose intolerant. I use rice milk in any recipe that calls for milk. I use rice milk in scrambled eggs and omelets. You can make puddings, cakes, cookies with rice milk.
I've started noticing a few foods in stores that state that they are lactose free. The most likely stores are the ones that cater to a healthy, green life style such as Whole Foods, Trader Joe's, Natures. Trader Joe's has a list of lactose, sodium and soy free foods. People who are allergic to the protein in milk are often also allergic to soy. This would eliminate cheese alternatives. Milk protein allergy is not the same as lactose intolerance.
Ask about the ingredients in Dairy Queens' ice cream. I am willing to tolerate gas in order to eat ice cream. I've noticed that having Dairy Queen ice cream never gives me gas. I've not investigated their ingredients. I also can easily tolerate the ice cream at McDonald's. I've not paid much attention to my symptoms at McDonald's but have wondered if the mix that these places use for ice cream is different in a manner that it doesn't trigger lactose intolerance. Having a protein allergy may also eliminate those sources of ice cream.
I've spent most of my adult life "testing" myself for food allergies and intolerances. I've learned over time that I can tolerate small amounts of some foods before I develop a noticeable reaction to the foods. Has your baby's doctor talked with you about testing foods to find ones that your baby may be able to tolerate? If you haven't talked with an allergist I suggest that doing so may help.
My granddaughter has been seeing an allergist that specializes in pediatric allergies since she was a baby. He and his staff have made helpful suggestions. A dietitian may be of good help for you since you're having to deal with your diet because of your baby. Some foods or small amounts of some foods may not get into your milk. I don't know. I studied nutrition in college and know that the way our bodies process foods is complicated. I've learned that I'm not allergic to dairy. I'm lactose intolerant but I can still eat small amounts of cheese and ice cream. Your body does not get feedback from your food intake. You have to rely on what you see in your baby. That makes it all more complicated.
I've discovered that sorbet does not have diary products but sherbet does. I've spent most of my adult life choosing sherbet over ice cream thinking it had no milk in it. I missed out on a lot of good ice cream :)
Of course, meat and vegetables do not have diary. You can fix them anyway you want except for the sauces. If you want to add a sauce to them, there are many really good sauces on the grocery store shelf. Or you can flavor them with any number of herbs and spices. Experiment to find the flavors you like.
I'm either intolerant or allergic to nearly every fruit and vegetable in the raw state as well as being lactose intolerant. I've never felt deprived or found it difficult to eat out. If milk protein or lactose intolerance is all that you're dealing with you'll find it easy to develop a way of eating that is not very different from your old way.
If your baby is just lactose intolerant (s)he may not react to baked goods, such as hamburger buns, at all. If she's allergic to milk protein she may depending on whether or not they use milk in making their buns. I'm lactose intolerant and I do eat commercially backed goods. Many baked goods have so little dairy in them that you may be able to eat them without your baby being affected. This is where a dietitian could be helpful. I want to note that I'm more tolerant of gas than many people are and definitely more tolerant than a baby is able to be.
This reminds me that one of the fast food restaurants is offering a hamburger without the bun. They put everything between lettuce leaves. I don't remember for sure which one does this but it may be Jack in the Box.
I think you'll be surprised at how easy it is to eliminate diary from your diet once you get used to it.
As for recipes: I use several sites on the Internet for recipes. Some are Betty Crocker, Pillsbury, Gourmet, Food Network, various Food Channel cooks. I think that if you Google diary free recipes there will be a site for that.