Once I oblige her, she likes to start off the pleasantries by sniffing and climbing all over my lap.

This involves a good deal of head-bumping and chirruping, which leads to ...

... the lateral shin snuggle. She'll sidle up to my calf, coy as you please. Before I know it, she's nuzzling my pant leg and giving me the sleepy eyes.
Finally, when Lily's decided all's well between us, she steps daintily into the kitty-shaped hollow my legs create and nestles from head to tail for a proper snooze.

My tailbone is protesting all the sitting, but the near-audible sigh of bliss Lily makes when she settles onto my knees is so worth it.