What is the difference between a lemon pound cake, a lemon loaf, and a lemon bread?

The difference is the person doing the naming. Seriously, you seem to be looking for clear cut categories where none exist.

If one of the same person calls three different things a "lemon bread", "lemon loaf" and "lemon cake", you can typically expect that the "bread" will be somewhat less sweeter, less aromatic and less fine than the "pound cake". This is probably connected to soda breads eaten in times of shortages (especially wars) which were then mixed with vegetables or fruit, but were not as fine as cakes. The "loaf" part may be more connected to the shape than to the batter type. But if two different people are doing the naming, all bets are off. So if you are looking for recipes, you should use all three search terms.

See also my recent answer explaining a bit more about naming.

Just to add to rumtscho's answer, there's no standard nomenclature. A similar item consisting of a cake-like thing baked in the shape of a loaf with a decent amount of sugar and eggs could be called any of the terms you use.

On the other hand, I'd say there are some trends in the use of such terms:

1. A pound cake traditionally refers to a cake made with equal proportions by weight of flour, sugar, eggs, and butter. (Traditionally one pound of each.) Again, traditionally, such a recipe is leavened through the beating of butter and sugar, trapping tiny air bubbles. Traditionally, no other leavening (e.g., baking soda or baking powder) is used, leading to a rather dense cake with a fine texture created by those small bubbles. If you use the traditional proportions, the result will be quite rich (lots of butter) and more "eggy" than many modern cakes. Pound cakes traditionally could be baked in a many different pan shapes, though ring/bundt pans or loaves are perhaps more common.

If you asked me to bake a "lemon pound cake" for you with no further instructions, I'd use the traditional proportions with no leavening other than creaming butter and sugar, and I'd add some lemon extract and/or other lemon bits like lemon zest. But the result wouldn't be like your linked "pound cake" recipes, other than perhaps being somewhat dense and with a relatively fine crumb.

Modern "pound cakes" modify the proportions quite a bit and often include baking powder and/or baking soda. Others include all sorts of random ingredients (as in the yogurt pound cake you link in the question). But if you search for "pound cake" you will likely find some recipes closer to the traditional version I mention.

2. A lemon loaf is admittedly a term I've never heard before, and I can imagine all sorts of things it might mean. The only citation you give is for something called a "pound cake loaf," which is obviously meant to reference a (non-traditional) pound cake baked in a loaf pan, as I said was an option above. A quick search for "lemon loaf" seems to indicate a large variety of types of cakes baked in a loaf pan.

So, I'd say the only defining characteristic is its shape -- something with lemons that's baked in a loaf pan. You could bake a lemon pound cake in a different sort of pan, but then I guess it wouldn't be a lemon "loaf."

3. Lemon bread traditionally refers to what I'd call a "quick bread." They are usually -- though not exclusively -- also baked in loaf pans. Quick breads are much more varied in their ingredients than traditional pound cakes, though they typically use a more simple mixing technique without the long beating required for pound cakes. Instead, baking powder/soda is used as the primary leavening, perhaps along with some acidic ingredient (like buttermilk or yogurt, or obviously lemons here) to aid in the rise. Traditional quick breads are often simply stirred quickly together and dumped in a pan, resulting in a more lumpy batter and ultimately a final texture that can be softer, looser, lighter, and with a larger crumb than (say) a pound cake.

But again, I'm working off traditional definitions. There's no reason a "lemon bread" recipe couldn't start with a more pound-cake-like template, or some other genre of cake. But if you search for "lemon bread" I assume more of the recipes will be similar to what I describe, compared to searching for "lemon cake" or other things.

I should also note that "lemon bread" could potentially refer to a yeasted bread too, which would be quite a different thing. It would likely still be somewhat sweet, but the technique and resulting texture would be completely different from a cake or a "quick bread" (which, despite its name, is basically a cake generally baked in a loaf pan).

To summarize, I think the difference between these terms lies not in what is common between them, because (as I noted) you can easily find similar results that would all use different names in their recipes. There's substantial overlap. I think the difference lies instead in what sorts of things might come up in a search for some of these terms but which would not qualify under all categories -- for example, a traditional pound cake baked in a bundt pan would not be called a "lemon loaf" or "lemon bread." A yeasted lemon bread would definitely not be called a "pound cake," nor likely would most "quick bread" type lemon loaves.

(Minor final note: I do disagree slightly with rumtscho that a "lemon bread" will typically be less sweet than a "lemon pound cake." Traditional pound cakes have so much butter and eggs that they aren't necessarily very sweet by modern (American) cake standards. And many quick breads I've had are quite sweet, but both cakes and "breads" can vary significantly. Nor would I say "breads" are necessarily less "aromatic," as quick breads are traditionally a showcase for ingredients from carrots to zucchini, and from bananas to lemons, such that quick breads often traditionally had a higher proportion of flavorful ingredients that would have disrupted the texture of a standard cake. But again, usage may vary.)