We haven't stayed CL at BC but we did at Poly. I would imagine they handle allergies in a similar manner.
DD10 can't have regular milk or soy milk. The chef in charge of the CL lounge ordered rice milk for her (that's her preference but I also know that WDW carries rice milk at many locations). The CL CMs would pour us a cup any time we asked. For DD13 who prefers soy milk they would hand us as many single serving cartons as we wanted any time we asked. They would typically bring us out 2 or 3 any time we asked for one and just told me to keep them in my room fridge for my convenience.
For your daughter, just ask for milk any time you want it. If you're wanting to avoid draining the jug by filling a few cups to bring back to your room in the morning (just use the coffee cups with lids) then ask a CM in the lounge. I'd probably just fill 2 cups in the morning; one for immediate consumption and one to put in the fridge for the afternoon; then in the evening go back and ask for another cup. Just use the coffee cups since those have lids.
I don't see why you should by milk when it's available in the lounge. There's no rule saying you can only have 1 glass per day.
Ask Special Diets if there can be almond milk for you in the lounge. They'll get a firm answer to you one way or the other from the CL chef in charge of allergies. They may or may not be able to; just ask. I've had better experience going through Special Diets rather than IPO; IPO doesn't actually check with the chefs while Special Diets does (at least that was my experience at Poly).
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