Just think of a lipless crank sort of like a spinnerbait. The only difference is you shouldn't use a lipless crank around any sort of cover, unless you like trolling over to snags and trying to jiggle them free. Saying that, I think the spinnerbait, and the lipless crank are probably the best search baits in bass fishing. Spinnerbaits cna be used in moderate to light cover around the shore to search for feeding or even holding fish, then when you mover out deeper, tie on a 1/2 or 3/4 ounce rat'l trap and do the same fan casting with the lipless crank.
I just started using ratl traps this season, and they are great for covering a lot of water, horizontally and vertically, especially in open water. They let you cover the entire water column, as long as you count them down after the cast. They have great vibration and flash/colors that will atrract fish.
To be more specific to your question, the best times are probably when fish are in a more agressive mood. There will be times when a bass will lunge from a distance and chase down a fast moving lipless crank, and there will be times when the bass will want a more natural slower stop and go retrieve of a floating or suspending billed crank.
Normally you'd throw a billed crank on a slower 5:1 reel and a lipless crank on a 6:1 or a 7:1 to really get that bait moving, the higher reel speed will pick up line faster. This is good if you work the lipless bait correctly and jerk and twitch it like instead on just reeling it back in. This more erractic action the bait will have will really send off a different vibration than just a steady retrieve. Jerking a bait forward and letting it fall can create a good amount of "slack line" which will result in lost feel. If a bass strikes your bait on the slack line, You may not feel it or get a good hook set. You want a good tight line to always feel your bait, so you can feel any strike you get or any structure or cover your lure may come into contact with.
Best bet is to start off fishing a lipless bait once you locate fish on your fish finder, or a spot that you think will be holding fish ( Over grass or weed beds, over deeper structure like humps, drop offs points, even right around shallower cover or structure like parellel to weedlines or lily pads, or docks), and if you aren;t getting any strikes with a lipless bait, switch over to a floating or suspending version of a billed crank and work a stop and go or a twitch retrieve, this should excite the bass into pouncing on your lure. Sometime the bass will already be excited and jacked up ready to kill anything that looks like it could be it's next meal. And other time's a bass will be neutral or negative and really need to be convinced that your lure is weak or slow and easy to catch until it will think about pursuing it.
I would say anytime you see a spot that is worthy of crankbait fishing, start off with a lipless bait, it is a great lure to cover the spot with and pick off the aggressive fish with. Then once the bite slows or the bait proves un productive, witch over to a lipped crank and slow down the retieve, or bottom bounce it to attract the fish, this is something you can't do with a lipless bait, you can't really bump things with a lipless bait either, since the bill is what usualyl deflects the bait saving a snag.