I like frozen treats like ice cream, but I do try to stay away from dairy as it sometimes ... well, that's not important. At least not to you. 

RIGHT so

Ice-cream-like frozen treat without dairy, which pretty much means sorbet. Which is frozen fruit juice. But instead of buying fruit juice in a jug, which is too thin really, buy it in the little cans of concentrate, generally in the freezer section of the grocery store.

Here's the tools you need.

• Ice cream freezer
• Stick (or other mechanical) blender

So here's the recipe.

• One can of frozen concentrated fruit juice. Any kind will do.
• One can of water (same can, just fill it up)

Just dump those in a big mixing bowl, and in a separate small container add

• 1/4 cup of white granulated sugar
• 1/4 to 1/2 tsp of xanthan gum powder

The xanthan gum is important as it takes the place of the milk solids and dairy fats which, in ice cream, get in the way of large (unpleasant) ice crystal formation. With xanthan gum, you get bajillions of tiny entrained air bubbles, which do about the same thing and makes the end product almost fluffy. If you want a more solid product, use less, but probably not less than 1/4, which is about where it starts having a useful effect. 

The trickiest bit is mixing in the xanthan gum, because as soon as you drop it in water it turns into goo. What seems to work pretty well is adding the gum powder to the white sugar granules and stirring that up really good, then adding a little water to the sugar and then stirring that up, then scraping the resulting goo into the juice and water. Use a blender to mix it all up real good. (I don't think hand mixing is going to properly disperse the gum.)

Pour it into your ice cream freezer and let the magic happen.

I like making sorbet from the cans of concentrate rather than from ready-to-drink fruit juice because I get a much stronger flavour. 

I've made most of the flavours (punch, berry, lemon, lime) available in the stores, except grape and orange. I haven't gotten to orange yet, and I dunno about grape sorbet. Maybe you'll take that chance, and report back, for the good of society.