Lycos owns the HotBot engine but doesn't utilize the Inktomi index. However, there's a link to HotBot from the Lycos pages, so if you're ranked high in HotBot, you may get some traffic through Lycos as well;
Lycos gets directory results from the Open Directory Project and paid listings from GoTo;
Lycos gets results from Fast for its advanced search features. It appears that Fast is now powering Lycos' main search results;
"Popular" listings are taken from reviewed sites and refined by DirectHit;