Sadly, the answer to the question "will lemons fade Melasma" is "probably not". If the condition you're dealing with is truly Melasma (as diagnosed by a Dermatologist) it is probably much too stubborn of a condition to be treated effectively with lemon juice. Happily, lemon juice is inexpensive and not harmful to skin so there is nothing to be lost by trying.
So what is the best treatment for Melasma? That does tend to vary by individual. It is best to start with your Dermatologist to see if what you are dealing with is truly Melasma. If so, he or she will have some recommendations about where to start. The best treatment for Melasma will usually involve the following:
Prevention: Sun exposure almost always makes Melasma more noticeable to a good high SPF sunscreen applied consistently will be necessary to avoid this. When out on the sun directly, the addition of a wide brimmed hat or visor is also a good idea.
Topical treatments: Some of these are available over the counter and some in prescription strength. These must be used in conjunction with the prevention measured discussed above to remain effective.
Skin procedures: Occasionally a procedure like a chemical peel, microdermabrasion, or laser therapy might be recommended by your Dermatologist. These procedures could have the effect of evening out skin tone or making the skin more receptive to the topical treatments mentioned above. A word of caution: many without medical backgrounds are now offering these procedures. It is best to use a Dermatologist with whom you are comfortable to perform or at least oversee these procedures.
So what about lemon juice for Melasma and other home remedies for Melasma? As mentioned above, some of these are inexpensive and safe so you can feel free experimenting. Make sure to do your research first as not all things advertised as "natural" are actually safe and often they aren't regulated.
The final conclusion is that your best bet is to work with a doctor you trust and to be vigilant about prevention and any treatments your doctor suggests. Melasma is a condition that will require your consistent attention.
Recommended Reading: Melasma: Is This the Clear Solution?