First of all - GOOD FOR YOU to never believe you're going to die. People can carry HIV dormant all their lives and it makes no difference to their health as long as they are well. It is believed that MANY people carry the HIV but don't even know it - it's only when they get sick that doctors say ... oh, it's because of HIV. Well, that really is a myth that needs to be explored more.
If this has launched you into a self healing/regeneration program, then that's going to stand you in good stead for the rest of your life.
No nut milk is included, however, if you don't want to follow it strictly, then you could always add nut milk ... it's good for you after all. Make sure you start off with raw (unheated/untreated) nuts, then soak them for around 12 hours, rinsing the water regularly. Then make your milk out of that (don't use the drained water). That way you'll have released the enzyme inhibitors and be drinking live nut milk, that's easy and quick to digest.
There are proteins in greens, but mainly when you use the whole green food, rather than the juice. I've researched some of this and if you eat whole, raw greens, the protein from that is in the form of amino acids that the body will make into true protein. Animal protein uses up a lot of digestive power and isn't true protein for the body, because the body has to prize it apart and then put it back together. As an example, if you ate 20 gms of animal protein, you will probably only extract 10 grams out of it. If you had protein in the form of amino acids as found in greens, your body can use all of it. (Think what gorillas eat and there lies the answer).
IF you are considering going outside of the specific protocol as outlined in the link above, instead of nut milk, consider blending greens with fruit. Mix approx 60-70% quality greens (like kale, parsley, spinach etc.) with sweet fruit to balance, add water and blend. Drink like a smoothie. This will give you plenty of protein. And it tastes good :-)
Whatever you decide, I wish you the very best of health!