There are multiple ways you can do this and/or setup server configuration(s) to accomplish this.

In a single droplet situation you can use a proxy server like NGINX or HAProxy to answer on ports 80/443 and route the traffic to the appropriate backend server/project - In your case this would be your LAMP and Java projects - Each of these project would need to be configured to answer on a different port then 80/443 like 8080, 81, this is up to you.

Here is a great start on how to do so with NGINX:

• https://www.digitalocean.com/community/tutorials/how-to-configure-nginx-as-a-web-server-and-reverse-proxy-for-apache-on-one-ubuntu-14-04-droplet

• https://www.digitalocean.com/community/tutorials/how-to-set-up-nginx-server-blocks-virtual-hosts-on-ubuntu-14-04-lts