Lemon is rich in fruit acids, that remove dead skin cells and bleach darkened/discoloured areas. I know lots of people use lemon on their elbows to lighten up the skin there so I don't see why it wouldn't work for underarms too. I mean it's a natural method so it's not exactly going to do any harm if you try it.
Here's a guide that I copied below detailing all the things you can use lemon for that I found on the internet. Apparently just always use fresh lemons, not bottled lemon juice as that could be harmful.
1. To lighten discolored elbows: Cut a lemon in half and place one elbow in each half for approximately 10 minutes. Lemon’s acids will gently break down the dark patches of skin so they may be washed away.
2. To exfoliate dead skin and diminish the appearance of freckles and age spots: Gently rub a cut lemon and 1/2 teaspoon sugar granules over the skin for a few minutes. Repeat at least once a week until the darkened areas fade.
3. Another way to lighten age spots: Simply sit with a slice of lemon applied directly to the area for 10 minutes. Repeat once a week until spots fade.
4. Lemon hair conditioner: Mix the juice of one lemon with one cup warm water and apply to hair. Allow to remain for a few minutes, then rinse. This will add fresh bounce and shine.
5. Dandruff treatment: Mix a few tablespoons of fresh lemon with warm olive oil and rub gently into scalp. Allow to remain for 15 minutes, then shampoo and rinse as usual.
6. For smooth, pretty feet: In a foot bath, combine 1 cup of lemon juice, 2 tablespoons olive oil, 1/4 cup milk and enough water to fill the basin. (You may also add a few drops of your favorite essential oil for fragrance, if you like.) Soak feet for 15 minutes, then rinse with warm water. Do this once a week for several weeks for noticeably softer, smoother feet.
7. Astringent toner for oily skin: Combine 2 tablespoons lemon juice, 2 tablespoons vodka, 1 tablespoon distilled water, 1 teaspoon witch hazel. Apply with clean cloth or cotton balls to skin, then rinse. Caution: Do not apply to broken skin, as it will sting! This formula will keep in the refrigerator for a week.
8. Lemon Juice Astringent Simple:
Simply squeeze some lemon juice into a glass jar, and dab some onto your face every morning, let it set for 10 minutes, then wash it off with warm water followed by a moisturizer. Fresh lemon juice will last for 4-5 days.
