I am glad the rabbit is holding on. This is very encouraging.
Now you need to be very mindful of not rushing things. This is a time where you need to balance the benefit of the chemicals with overloading by using too much chemicals and causing poisoning. Signs of adverse reactions will help you and the vet recognize oxidative stress.
I would suggest leaving the lime juice out of the mixture. Your rabbit doesn't need to be drinking an acid mixture. Just put the sodium chlorite in water and go with that.
If you want to improve the absorption of the sodium chlorite you can mix the sodium chlorite and water in larger amounts and let that sit for 24 hours before giving it to the rabbit. This mixture will keep for a year or so and only needs to be kept out of UV light. Mix up a liter and fill the syringe for drinking from that.