Actually, according to the link above, the biggest unsupported browsers are Safari & Chrome for iOS (1.03% total), followed by Internet Explorer (0.60% total), Firefox < 64 (0.48%), and desktop Safari < 13.1 (0.44%). Some of these are probably bots masquerading as browsers, but Lynx isn't listed at all.
I'm not saying that webp shouldn't be used, but I think it makes sense to have a fallback in place for just a bit longer.