You use .webp images instead of .jpeg or .png or whatever they are at the minute, it’s as simple as that. It’s just an image format, so you save images as webp or you convert them using a converter (see Google, there are a million and one image format converter sites).
Note you can probably ignore that recommendation if you want your stuff to be viewable on iPhones because mobile Safari doesn’t support webp images (neither does desktop Safari, IE or earlier versions of Edge, Chrome, Firefox etc).
Lighthouse is designed to check if a site is ready to use as a Progressive Web App, which is mainly Google’s thing, which means it’s optimised for Chrome over everything else. Bear that in mind when you use it: it’s very good, but Google have ulterior motives