I’ve done a fair amount of Node deployments on a LAMP box. (I have a well priced, grandfathered dedicated server at Liquid Web). You’ll need root access, or someone at the service will need to do a lot of configuration for you.
Installing Node and Mongo is pretty easy once you get a package manager running. (Yum for Centos) The hard part is configuring Apache for Node, web sockets, and restarts. I’m happy to share what I know; however, I haven’t done a full Meteor deployment on a LAMP box.