It is definitely possible to install a Ruby on Rails app alongside the LAMP-stack. Though there are a few things to keep in mind. In particular, only one process can bind to port 80 at a time. So how you set them up depends on how you are already are running the Rails app.

There are a few ways to approach it. If you are running the Rails app behind Apache using something like Passenger, then just adding a new virtual host should work fine. These tutorials should point you in the right direction:

• How To Deploy a Rails App with Passenger and Apache on Ubuntu 14.04

• How To Install Linux, Apache, MySQL, PHP (LAMP) stack on Ubuntu 14.04

• How To Set Up Apache Virtual Hosts on Ubuntu 14.04 LTS

If you run it behind Nginx, using the LEMP stack rather than LAMP might make more sense:

• How To Install Linux, nginx, MySQL, PHP (LEMP) stack on Ubuntu 14.04

But you could also proxy from Nginx to Apache:

• How To Configure Nginx as a Reverse Proxy for Apache