LAMP is only the stack on the server-side. You can build rich JS applications on the client-side, and wire it AJAX to any backend you desire - Node, PHP, Python, Java... Any of these can be used to create a server-side API, REST or otherwise.
L - Unless you're an avid .NET supporter (declining rapidly, according to StackOverflow C# figures), you'll probably be using Linux.
A - Unless you're really picky about the http server, Apache has a decent offering. It's still the most popular HTTP server, and doesn't look like it's going anywhere. Even if you use Node, it's still probably a good idea to stick Apache/nginx in front of it.
M - And if you choose a relational DB, chances are you're gonna use MySQL/MariaDB. Despite all the noSQL buzz, it's still tricky to really use a non-relational one for transactions. Most people still fall back on MySQL as the main DB for transactions, and perhaps only use the cooler non-relational stuff for the non-critical stuff.
P - I think people hate PHP for the amount of bloat/inconsistent syntax and outdated server-side MVC frameworks. Of course, you may choose to use Node, Go, Java... but all languages have nasty parts, it's just a matter of how many people bitch about it. To be fair, NodeJS has quite a few nasty parts too, most notably the infamous callback hell.
So, even if you hate PHP with a vengeance, you probably can't run away much from the rest of the LAMP stack. Maybe you can replace one of two of the tech in that stack, or even all of it just to prove a point, but the main idea on the server-side remains the same: OS, DB, Application, HTTP server.
