Let's look at the two most prominent nutrients found in lemons that could play a role. These are vitamin C, and citric acid.
Lemons are rich in vitamin C. One fruit will deliver from 50% to 75% of the daily recommended amount, depending on the size of the lemon. That's nice, because it is an essential nutrient; humans can't synthesize it in their bodies. Now, does it promote fat loss? Doing a search yields a lot of articles that seem to state so, but many of them are from sources that I deem questionable at best. The source of this idea seems to stem from one study, conducted at the Arizona State University. Here is a link: http://www.ncbi.nlm.nih.gov/pubmed/16945143
The study observes that fat oxidation was reduced in the test subjects who had a vitamin C deficiency. Note that this does not mean extra vitamin C is going to increase fat oxidation, it only concludes that there appears to be a correlation between vitamin C deficiency and slower fat loss. Articles reporting on such studies often make faulty leaps in logic. They think "if a shortage of something reduces fat loss, then a surplus it of will surely accelerate it!". Unscientific. However, you'll want to avoid a vitamin C deficiency and lemon juice is a good way to do it.
So then there's long-term effects. Although long-term consumption of excess vitamin C could be harmful, there's no reason to believe that one lemon each day on top of a regular diet comes anywhere close to such an excess. In fact, there's common foodstuffs much richer in vitamin C which you can eat frequently without any cause for concern.
Onto the citric acid. There is a metabolic pathway in your body called the "citric acid cycle" that plays a major role in the energy supply to tissues, not in the least your muscles. One of the metabolites needed in this cycle is citrate, a derivative of citric acid. So getting some extra from your food seems like a good idea.
Anything bad about citric acid? Dosages that are too large can cause side-effects, but again, one lemon is not going to get you even close to that amount. You'd probably have to take medicinal concentrations to be at risk. The only long-term effect I can think of is that frequent consumption could affect the tooth enamel. Since you're adding sugar and salt (creating a sort of homebrew isotonic drink) it could be comparable to some sodas, although I suspect your drink is less damaging to teeth than, say, a cola. If it worries you, perhaps use a straw, or avoid letting it wash over your teeth when taking a sip.
EDIT:
I'll add another consideration. Apart from the vitamin C and citric acid discussed above, lemons also contain specific polyphenols. Here is a study that investigates the effect of those polyphenols in modulating the weight gain in mice when provided with a diet that would induce obesity: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2581754/
The conclusion of the study is that a positive effect can be seen in reducing weight gain in the form of fat when supplementing the diet with these polyphenols. Since this is a study on rodents you can draw no hard conclusions on how it will affect humans, and it wouldn't prove that lemons would actually assist in weight loss, it only suggests they can have a positive effect in slowing weight gain.
So in summary:
- There is a lack of evidence that your drink will assist in fat loss.
- Current evidence suggests that the polyphenols in lemons can assist in reducing fat gain.
- There is evidence that a lack in vitamin C will reduce fat oxidation. In this case the lemon drink would only help if you are otherwise deficient in vitamin C.
- There is no reason to suspect that drinking the juice of one lemon daily would have negative long-term effects.
This leaves us with the sugar and salt. If the sugar is not in excess of what your target for daily carbohydrate consumption is, and doesn't negate a caloric deficit, then it's fine. If the salt doesn't put you over the daily recommended allowance for your sodium intake, that too is not a problem.
I foresee no negative long-term effects but there isn't hard evidence that it will assist in fat burn. So it's a case of "if it doesn't help, at least it's not going to harm you".