Well it's certainly unusual, so could be called 'weird'. I've never met anyone or even heard of one who has one eyelid.
If you have one eyelid for any reason you're probably unfortunately gonna have to get tough to insensitive and ignorant people .
I don't see how eyeliner for one eye is any different than 2 eyes. I doubt there are well known procedures for one eyelid.
Could you maybe elaborate on the circumstances you're talking about?