The term "lover" is gender-neutral. A man or a woman can be someone's lover.

Lover is a gender neutral term. Another one would be partner or significant other, because there is not a specified gender within the term like there is with boyfriend or girlfriend. Everyone can be referred to as a lover in a relationship, but I often hear people call their boyfriend/girlfriend their partner instead. Lover is more intimate, and can sometimes assign a different connotation, especially if there is very little context. Sometimes saying that "she is my lover" can mean, or be interpreted as "she is my mistress." It all really depends, but mostly people stick to boyfriend, girlfriend, or partner. Hope this helps! Cheers :)