The pelican hook you show has a locknut, the eye doesn't seem to. IMHO, if the locknuts are set up snug, you're good - particularly if you get into the habit of seeing if the locknuts are loose now and then. If you find loose locknuts too often, then I'd think about locktite. Start with the blue stuff - the red stuff needs heat for disassembly.
Oh yeah, leave a little slack in your lifelines - you're not building a piano.