They had become so corpulent as to not have laps on which to place the napkins.

When Anne Boleyn was presiding over her coronation feast, there was a noblewoman whose job it was to hold a napkin up in front of the queen's face in the event she needed to spitthat's all I've got.
Of all sad words of mouth or pen, the saddest are these: it might have been. - J G Whittier

In all the dinner/feast/eating at table scenes, why do people of this period drape their napkin across their left shoulder, as opposed to across the lap?
I definitely prefer the more discreet way we do it today. I wouldn't want to see dirty napkins hanging on people while I ate dinner.
In the "The Last Supper" painting several people shared one long napkin:
http://www.amolenuvolette.it/root/image/abrupt_clio_team.folder/quotidien dans la peinture occidentale.folder/015[amolenuvolette.it]1464 1467 dirck bouts la dernière cène%2C panneau central du triptyque.jpg
Eew!

Ha! I missed that altogether. And I've just noticed that the lady in grey, on the left, does have the napkin over her lap.
Call me Ishmael

In that painting, at least 3 people had the napkin draped over the left forearm. Two guys in black facing us and the guy in brown with his back to us.
(I had a job trying to tell the men and women apart in that painting!)

In all the dinner/feast/eating at table scenes, why do people of this period drape their napkin across their left shoulder, as opposed to across the lap? Does it make it easier to wipe one's hands during a meal that's partially eaten without aid of utensils?
I'm not sure there's a huge difference in convenience. Perhaps it was more comfortable given that the napkin was larger then than now.
Interestingly, in this painting, dated to the end of the 16th Century, only the
men
drape the napkin over their shoulders:
http://www.geffrye-museum.org.uk/_image/OAIZWHXK.jpg
.. and Sir Henry's napkin isn't visible. Presumably he and the women have their napkins in their laps. Perhaps this came to be considered more discreet and therefore more refined, and for that reason preferable, but in truth I doubt the history of etiquette is ever that rational and straightforward.
See here for interesting examples:
http://paper2play.blogspot.co.uk/2008_09_01_archive.html
Call me Ishmael