I believe why we breeders caution folk that Savannahs are not lap cats is NOT because they lack affection, nor that they won't CHOOSE to climb into your lap when THEY want attention....it is because cats that are more considered "lap cats" are the type of cat you can pick up and put on your lap and they will stay. My British Shorthair will stay if I do that as long as I am petting him, while my Savannahs would immediately leap off. They choose when it is cuddle time, the human does not.
Working in Rescue, we get lots of emails asking for advice in handling their new Savannah kitten. We do get asked "when I pick up my kitten they want to get down immediately, how do I train it to sit still on my lap?" and hence we have to explain that a high energy kitten wants you to play with them and then they might come cuddle afterwards.