Are you sure lynx doesn't fetch any external resources? Some text-mode browsers (I forget if elinks or w3m does this) fetches external CSS by default so they can attempt to render fonts on the the 16-color terminal. :)
The "right" way of doing this (calling lynx in a network-restricted cgroup/chroot/container) sounds like a pain.
Lynx doesn't support images, CSS or script. It does support cookies and redirects (by default it prompts for both). Basically, it renders the bare HTML of the page you open, without fetching external resources. If you find it behaves differently, make sure your lynx command isn't actually symlinked to links (or another text browser with graphical/enhanced capabilities).
The "right" way of doing this (calling lynx in a network-restricted cgroup/chroot/container) sounds like a pain.