USE="doc" sqlite-3.3.6 does not install images linked from html pages. Changing: dohtml doc/*.html doc/*.txt doc/*.png to: dohtml doc/*.html doc/*.txt doc/*.gif art/2005osaward.gif fixes this.
Fixed in my dev overlay: https://overlays.gentoo.org/svn/dev/betelgeuse/dev-db/sqlite
3.3.12 committed and it has the fix for this