Why specifically 'with paddles'? The vivid and picturesque thought that has seemingly gone into this question is slightly worrying. And for that matter, why specifically for 'lying'. There's much, much worse things than lying. Heck, depending on the context, lying can even be good.
Anyway, I think physical punishment is okay in rare circumstances. It's natural, though as humans parents should show self-control and restraint. All sorts of animals teach their offspring using physical warnings. In a way, it's a necessity for the learning of a child/animal - at some point, all people have to learn that certain actions can have consequences that may include pain. They have to learn that certain ways of behaving towards people will cause them to react appropriately. Cats are my only example (not really familiar with the nurturing habits of any other animals) - they're generally patient, but if one of a cats kittens does something to hurt the cat (or steal it's food, since this species does have a pecking order after all), the cat may respond by a light swipe and hiss or even by biting the scruff of the kitten. It doesn't cause them much pain, but does send the message that pain is a consequence of such actions.
I think bringing out a paddle, belt or ruler is way to extreme and not to mention impersonal for anything, though. You certainly shouldn't be using such force that your hand is at risk of getting hurt from inflicting the punishment, so why the idea would even come about just puzzles me. Also it'd require going and getting the paddle, by which time the need for physical punishment is over. It should only be a quick, very light warning, for very severe circumstances (the child is actually endangering or hurting you, themselves - though obviously not if they're hurting themselves as the punishment is self-serving, or someone else). If you have to think about it, you probably shouldn't do it. If you go to get a weapon, you possibly need psychological help...
I don't think spanking kids with paddles is an appropriate punishment for lying children. There are far better ways to punish kids and actually teach them a proper lesson, than physically abusing them with a paddle. Taking something away such as a video game or television privalages for a prolonged period of time can be more effective.
I think those days are needed but yet to a limit, its best to talk with your children and get an understanding, paddles and spanking is not always the right answer and sometimes the physical punishment can leave a long time or forever imprint on that child even when they become an adult.