Hosting a website on a DO droplet and Github Pages

You would need an extra droplet or other server to act as a proxy/load balancer. You can set up a small droplet with nginx and configure it using a configuration like the one below:

upstream lb {
    server server1.com:80;
    server server2.com:80;
}

server {
    listen  80;
    server_name localhost;

  location / {
        proxy_pass              http://lb;
        proxy_redirect          off;
        proxy_next_upstream     error timeout invalid_header http_500;
        proxy_connect_timeout   2;
        proxy_set_header        Host            $host;
        proxy_set_header        X-Real-IP       $remote_addr;
        proxy_set_header        X-Forwarded-For $proxy_add_x_forwarded_for;
}
}