Can I create a firm mousse (dense self holding foam) with juice and no fat or dairy with my cream whipper?
It's very difficult to create a firm anything with a cream whipper, since by definition what it does is whip. It's meant for preparations that incorporate a lot of air - i.e. light and fluffy. Most mousse recipes don't only use cream, they also use eggs and/or gelatin and that is what gives it its body.
There are certainly ways to whip things without cream - for a gel preparation (as opposed to a foam) you're generally looking at egg whites (or equivalent), gelatin, or carrageenan. Gelatin is already a very common ingredient in mousses, but I think carrageenan might be a better choice for what you're trying to do, because of its shear-thinning property; whereas with gelatin you have to heat it in order to loosen it up, carrageenan you can just shake a bit.
I think you'd do well to start off with a meringue-based mousse and forget the whipper, just to see if it's a texture you like. You make the base and then fold in the other ingredients. It's not going to be the same as a traditional mousse at all, but nothing will be without fat. Italian meringue has more of a frosting/icing-like quality, so you could try that as well.
Then you could try incorporating iota carrageenan (kappa isn't shear-thinning) or gelatin. I don't think I'd recommend a whipper for this, though. Typically you'd make this by first preparing the meringue, then folding in egg yolks and other flavours. The gelling agent would probably go in with the latter half, since I'm not sure if it's possible to whip egg whites with gelatin or carrageenan already incorporated (I've never tried, but it sounds dubious). If you do it in a whipper, I'm not sure how you could separate these steps. You could try to do them together if you don't mind the possibility of throwing away ingredients; my guess is that it might fail to whip at all, or if it does whip, then might be too thick to dispense.
You might also consider more traditional dairy substitutes - for example, there's a recipe for coconut oil chocolate mousse that you should be able to adapt to fruit. Coconut oil is a fat, of course, but I'm assuming your real issue is dairy - you don't explain your reason why you can't have fat or dairy and without details, it sounds like an unnecessarily arbitrary restriction - if this has something to do with not wanting a "fattening" dessert then it's the sugar, not fat, that you should be concerned about.
Anyway, one last thing - you probably will not meet with much success trying to use actual juice for this. I suggest using an extract and some food colouring if you want it to look right - or maybe some frozen juice concentrate, so you don't need to use as much. If you're whipping egg whites, you can't water it down, and you don't want to lower the pH too much either.
Aaronut's answer is spot on, and gives lots of details, but if you are not experienced with foams, you might need some more general information before you read the details.
The simple answer is: no, you can't. There are very few substances in the kitchen which do foam, and even less whose foam doesn't dissipate after a few seconds.
The two most common foams in the kitchen are whipped cream and meringue. Whipped cream works because cream is a fat-based emulsion; you need at least 30% of fat in your food to create this type of foam (and, if it isn't already emulsified the way cream is, you might need to add emulsifiers, such as the egg yolk in mayonnaise).
The second common foam is meringue. It is protein-based. As Aaronut's answer says, it only works as long as it is not watered down. If you add stuff to it, the proteins cannot hold to each other any more, your additional liquid gets in the way. This is why he suggests working with an extract and food coloring.
Any other foam must be created by adding a thickening agent capable of achieving firmness, and forcing bubbles into your mixture. A cream whipper cannot force bubbles into anything; it does mix liquid with air, but it only creates bubbles if it is a bubble-friendly liquid like cream or egg whites. You'd need a special foaming device and thickeners to firm the foam. This is what the other part of Aaronut's answer explains - the gelatin/carrageenan part of it.