webp is an image format, like jpg / png. since it's a static file, litespeed won't cache it, just serve it directly. litespeed only cache dynamic page.
just tested latest lsws 5.1.11, it can serve .webp well just like serve a jpg/png image.
for web server to support webp, just need add an MIME type "webp image/webp"
for very old version of lsws, you can add it in .htaccess:
AddType image/webp webp