There exists no modern web browser using Motif as its UI toolkit. However, there are fewer challenges there than may initially be apparent, because this exists: https://bitbucket.org/chromiumembedded/cef
Chromium Embedded Framework provides a browser engine without making assumptions about the UI layer; one particular way it can be used is to hand it an X11 window (which is distinct from a toplevel "shell" window with a border and such -- think "surface") to draw to and wire in callbacks to control it, so it can work with any UI toolkit. I wouldn't say it's "easy" to make a browser this way, but it's certainly practical.
There exists no modern web browser using Motif as its UI toolkit. However, there are fewer challenges there than may initially be apparent, because this exists: https://bitbucket.org/chromiumembedded/cef
Chromium Embedded Framework provides a browser *engine* without making assumptions about the UI layer; one particular way it can be used is to hand it an X11 window (which is distinct from a toplevel "shell" window with a border and such -- think "surface") to draw to and wire in callbacks to control it, so it can work with any UI toolkit. I wouldn't say it's "easy" to make a browser this way, but it's certainly practical.