@Street, LAMP is much more than pure HTML. Serving HTML is literally just spitting out text over TCP/IP. LAMP implies a database, a server-side scripting language, a specific HTML server (all you really need), and the Linux kernel. It's not entirely surprising that the RPi would choke on not only running a complete kernel, but also a fairly inefficient HTML server, database AND scripting language. It's a problem that screams for a parallel solution, but being run on a single-core device.
On the other hand, if you just want to handle HTML, you just need to be able to speak TCP/IP and vomit text documents. As pimath points out, the Arduino has been demonstrated to be able to do this, albeit with an ethernet shield. So, practically speaking, it's not so crazy to suggest a self-hosting ez8 site.