Change default web browser to lynx from terminal

First make .desktop application for lynx:

[Desktop Entry]
Type=Application
Name=Lynx
Exec=gnome-terminal -e 'lynx %u'

And save it to application directory e.g /usr/share/applications/ naming like lynx.desktop and give it execution permission (chmod+ x).

Then set it as default web browser by using:

xdg-settings set default-web-browser lynx.desktop

Now try to Open link and it will be open with lynx in the terminal.

Note: lynx is command-line web-browser and hence it needs terminal so-that I've used gnome-terminal in my example Exec command. Your terminal application may be different. This works for me with my current system.