I would say the most essential applicance to have for doing raw food is a good blender. You could get away with just having the blender and no food processor.
Dehydrators are not necessary to do raw. They are sometimes called the 'raw foodist oven'.
Juicers are another raw food applicance that are not necessary but if you want to drink alot of juices - they are good to have.
Another good thing to have is a coffee grinder to grind up nuts or seeds or raw chocolate. But you could grind these in your blender too.
For the citrus fruits, unless the fruit is the main part of the recipe, you may be able to skip that ingredient. I am not sure of a sub for those. If you are trying to get the recipe sweet like for oranges, there is agave nectar. It is like honey but vegan and you can buy it raw.
For sour for the lemons, you could try a bit of apple cider vinegar maybe.
There are lots of other fruits and tons of raw veggies to eat on the raw diet. Plus, there are raw nuts and seeds and sprouts.