The main limitation is number of clients here. If you have a RESTful API, some ETL loaders, and several webservers running on EC2 all talking to your database, then you need a real client-server architecture.

However, if you're running your website on Apache, on a single webserver, then there's really only ONE client for your database, in which case SQLite works great, even if there's a heck of a lot of load.

SQLite is fundamentally a C library talking to a binary file format, so it's orders of magnitude faster than making a network connection to a client and then issuing SQL.

I've run medium-sized websites on an MVC framework talking to SQLite MANY times, and it works great.