I heard there were some forks of Brave trying to do that ( but they did not work as they were related to a social media platform with bad reputation )
I also know opera has a bitcoin wallet but it is not lightning.
There are some chrome extensions, Joule has some good rating.
I am trying to add it to an Electron based browser I have and I am wondering if it's a good idea, why it's not and so on.
I envision it as easy to access and make web payements with lighining. Users would just deposit small amounts in it.
Security would be a concern.
flash.pm is my browser.