Begin by peeling the apples (leaving the peel on makes the texture really unappealing--gah, I punned!) and removing the core. (easiest way I've found without a corer-- just slice them in half, and then cut wedges, avoiding the middles). Roughly chop (size doesn't really matter, but bigger bits require longer cooking time. It’s up to you.
Put them in a pot along with the water/juice and lemon juice. Bring to a simmer, then add your cinnamon, vegan sugar, and cloves.
Cover the pot, reduce heat to the lowest setting, and go do something fun for half an hour. No need to stir or remove the lid. After 30 minutes, give it a stir, and then find the whole cloves (if using) to throw away (not so important if adults are eating it, but you should definitely pick them out for the children).
At this point, if you've got a handheld blender (or even a normal one) blend away until the texture suits you. If not, the apples should be soft enough to mush up with a potato masher or a fork-- it makes the sauce quite rustic anyways.
Serve hot or cold, and try variations. This is just a basic recipe; almost all fruit can go into a sauce like this. You could substitute other hard fruits for the apples to make a pear or nectarine sauce, or just add a cup of something else to make apple-strawberry or pear-mango.
Because of the vegan sugar and spices, it keeps for a week in the fridge, so go ahead and double up on the recipe, just remember to stir before serving if its been in the fridge for a while.