It's carrot cake - and you can't eat that, either 
. I just posted on your other thread actually. If she's content that's a great sign and I personally wouldn't consider medicating in that case, provided her weight picks up.
If you give it a go, you need to cut out everything that's made from cow's milk, so the obvious stuff - butter, yoghurt, cheese, even spreads with buttermilk - so most margerine spreads. Anything with casein, skim milk powder (check labels on biscuits, crisps, breakfast cereals, anything pre-packed). Tinned or packet soups usually have cream in, fresh pasta often has cheese in, as does pasta sauce. Even things like bread and crumpets (I love crumpets!) have milk in. Some coatings - say onion rings or scampi have milk in. If you're eating out you need to get the restaurant to check. Consider pizza with BBQ sauce instead of tomato and no cheese and your normal topping - it's delicious! Most packaged foods nowadays have allergy advice so avoid things which say they have milk in on the allergy list, although things which say they're made in a factory which uses milk will be ok. The "free from" aisle at your supermarket will become your best friend.
Lacto free milk is not suitable as it's not a lactose intolerance, it's a cow's milk protein intolerance which is quite different.
Consider rice milk, oat milk or soya milk (although I personally avoid soya). Rice milk is nice on cereal but tastes quite different. I also like it in tea, but I've used rice milk for years so I'm used to the taste. Oat milk is slightly less sweet and needs a really good shake before use. Either way consider choosing the version with added calcium for obvious reasons, and keep up your calcium with calcium rich foods (Google this).
I did try my own BM in tea but didn't like it. A step too far? Maybe, but the usual alternative is just the lactation of another species so I don't care! But I didn't like the taste, not to mention it's ok doing the squirt in my own kitchen, but I didn't think I'd feel happy about doing it in the canteen at work . LOL. But it may work for you.
I use Vitalite dairy-free spread which isn't bad if you're used to spreads rather than butter. Sainsburys do a free-from spread which is healthier (Vitalite is full of palm oil which I normally try to avoid) but it doesn't taste of anything.
Booja Booja for chocolate or dairy-free from the free-from aisle.
If you want to try this and want ideas for alternatives just start a new thread and I'll look out for it (may then be useful for others).