When it comes to home "cures" for age spots, little is recommended more than lemon juice. However, evidence to its effectiveness is largely anecdotal, and applying lemon juice directly to your skin may do more harm than good.
Vitamin C as a Skin Bleaching Agent
One of the most common reasons lemon juice is cited as a skin whitener is its high vitamin C content. Vitamin C raises glutathione levels in your blood, a compound that helps determine skin pigmentation. Higher glutathione levels have been linked to lighter skin pigmentation. In one study, giving a cocktail of vitamin C, L-cysteine and vitamin E to guinea pigs caused their skin to lighten. However, this link only exists when vitamin C is taken orally. Topical applications, like lemon juice, are unlikely to raise glutathione levels and cannot necessarily spot-treat age spots. ["Effect of Simultaneous Administration of Vitamin C, L-cysteine and Vitamin E on the Melanogenesis." BioFactors]
Lemons Contain Alpha-Hydroxy Acid
Lemons contain citric acid, an alpha-hydroxy acid (AHA) that is an antioxidant. AHAs have been shown to help reduce the appearance of age spots over time. In that respect, lemon juice is effectively a chemical peel. However, while a little bit of acidity can benefit your skin, lemon juice is overall too acidic. It will dry and damage your skin instead of helping it. [Hanan Taha, M.D "How PH Affects the Skin."]
Lemon Juice Can Cause Sun Poisoning
In fact, lemon juice will actually cause photosensitivity. Compounds in lemon juice will react with sunlight and cause photodermatitis. Photodermatitis, also called sun poisoning, is painful and can blister. This kind of skin trauma can actually lead to further formation of dark spots. Dermatologists caution against putting lemon juice on your skin. ["Beyond Sunburn: Photosensitivity" Advanced Dermatology]