My magnificent beast Mimi would do the lap thing.
She'd see an open lap, and make a running leap for it.
She'd land lightly, which was amazing considering she was sorta heavy and all muscle, and then stare intently into your face while purring loudly.
She was a long-furred kitty, and very meticulous about her grooming.
She loved being fussed over, but if she was washing, she got really ticked if you dared touch her -she'd have to begin all over again because you 'soiled' her with your 'contaminated' human hands.
;-)
LOL I had a cat like that back home. I named it mignight cause it followed me home at midnight and it was solid black, but she eneded up being Jesse. She died a few years back. Very meticulous in her ways. And she did not appreciate extra attention while she was busy. LOL