Many browsers allow you to create a private browsing profile, which means that browser history, cookies, site data, etc. are deleted when you close the browser.

In Luakit there are already commands to clear history and data. There could also be settings 'Never remember history' and 'Clear browser data on exit' in history.lua and clear_data.lua, and whenever the last browser window is closed, it would check them and call the corresponding commands.

Right now, there is a workaround: write a bash script to start the browser, and after it's closed, rm -r the directories in question from .cache and .local/data. But in-browser settings are more elegant, in my opinion.