It could be unisex. I understand Lindsey/Lindsay started off as a boy’s name, and then it became popular for girls in the 1980s, and now it’s considered “too feminine” to give to boys since then. Now Lindsey is thought of as a girl’s name, no longer for men.
I personally don’t desire the name much for a boy, it’s more feminine in my book. However, it’s really up to you. I wouldn’t stop someone from using a name on a kid that seems wrong. Name your son Lindsey if it really means something to you. I would probably hope that child stands up for himself when he’s getting bullied.
If this was 1980 right now, it would feel like Lindsey is a boy’s name and we would be worried that it’s going to become strictly feminine. But that has already happened. I don’t think John is going to become a girl’s name since it’s more of a biblical name, not a surname.