Akoisexual (more commonly called lithosexual) is a sexual orientation on the Asexual spectrum. Someone who is akoisexual may experience sexual attraction but does not want it reciprocated. The akoisexual individual may be uncomfortable at the thought of someone being sexually attracted to them, or they may lose their sexual feelings if they learn it's reciprocated. As such, akoisexuals do not feel compelled to seek out a sexual relationship. Like with any sexual orientation, akoisexuals can have any romantic orientation.
Akoisexual can be a sexual orientation on its own or can combined with other orientations. For example, one could be akoisexual and heterosexual, meaning that when one does experience sexual attraction it's only towards individuals of the opposite gender.
Due to a claim of appropriating lesbian culture some individuals have attempted to replace the term lithosexual with akoisexual. This is due to the fact that litho- means "stone". In the lesbian community a stone lesbian is a lesbian who is okay with being the giver of sex acts, but not with being the receiver of sex acts. Because of that "lithosexual" could potentially be interpreted as being related to this term.
There has not been any consensus about the term, both in the asexual and lesbian community. There is no apparently evidence that the specific term "lithosexual" was ever commonly used by lesbians. Currently lithosexual and akoisexual are used interchangeably.