Yeah, red color lipstick will look good on fair skin.
For fair skin, coral reds or dark reds with blue undertones will be proper color. You need to find the right shade, if you have thin lips go for a lighter shade and if you have big lips go for a darker shade or a medium shade.
When buying lipstick, don't forget to consider lip liner, especially when buying red shades. Picking the perfect red lipstick is also more important.
Red is a very trendy color and would look great on fair skin; it is the color of passion, the color of love. It would give a bold, dashing look to fair skin women with pinkish or rosy hues rather than pale or yellowish skin tones.