Every cat is a bit different, my previous cat Meme who the girls where I used to work rescued when the saw her hanging around.
She chose me, She would climb in my lap and press her head against my chest.
This was to let me know she wanted a hug, I'd give her a nice long hug and then she'd either settle down in my lap or right beside me in my chair for some quality time together.
Now Samantha, my recently departed Maine Coon cat, wouldn't sit in your lap but liked to sit or lay on the arm of the easy chair and be petted brushed and combed.
My remaining cat Chiquita who my ex rescued when she was hanging around our home is very vocal and needy, she won't sit in your lap either but demands to be petted and if you get up she'll take a no claw bat at you to show her displeasure.