I once had the dearest Old English / Dutch cross bantam rooster. His siblings were killed by a predator, and he was all that was left (although they *all* were sweet) so I had just him for a couple weeks. He would flutter around the yard following me, never ran away when I went to pick him up, and would perch on my arm until I took him off. I never thought to put him on my lap (he was so tiny!), but I'm very sure he would have stayed right there. I once even put him on my scooter handle (oh my gosh, I used to scooter around, that was about 4 years ago, it feels so long ago xD) and he stayed on except until it started to get too bumpy. I don't blame him. Oh and yes, his name was Scooter.
Now he, and his siblings were special. I'm pretty sure they must have been pretty cold as chicks, because more often than not I was holding them. I held them as I did school (oh, the perks of homeschool!), and in all my free time I would go in the bathroom and shut the door to keep out the other pets and hold them and perch them on my fingers and arms. I would also sit for hours with them as I played games on my laptop. When it was warm outside I'd go read a book, lying on my stomach in the sun with them, and they'd romp around and then come back to me. Once I had a silkie who had chicks and I realized their actions were similar to my chicks. I suppose mine imprinted on me pretty well.
Oh gosh that was a long post down memory lane, so sorry. But basically, yes, lap chickens can be a thing, but the more you handle them the higher your chance is. I also coaxed a silkie to sit on my lap. Catching her was hard, but once I had her, she'd actually sit on my lap. Go figure. All my other chickens prefered perching on my arm, shoulder, or back. And no, that last one wasn't very comfortable!