Lithium-ion batteries should not be discharged below 3V. Which is not a concern of you as the user, as the control circuitry will report it as 0% much earlier, and will cut if off completely if it ever goes near that value. The only concern is, theoretically, keeping the battery at its maximum volatege (4.2V) constantly. So there is a grain of truth in “don’t charge above 80%”. But you would need to carefully plan charging through the entire lifespan of your phone to prevent that, while risking it will run out of juice when you need the phone most. So hardly worth the effort.(1) Turning the phone off while unused will of course reduce energy use and wear in general: nothing to do with li-ion cells in particular.
NiCd batteries didn’t have memory effect either in normal use. The effect was only present in very rare scenarios not found in consumer gear and wasn’t an actual drop in capacity, but a perceived one due to not charging the battery fully.
(1) Said by a person, who does that out of habit. Unless I need something to contain maximum charge, I disconnect devices as soon as I see they are fully. But that’s more satisfying my brain than actually changing something.