He's asking about the position of the lens while in storeage, not where to store.
I don't think there's any long term issues whether you store them standing up or lying down cos lens are "supposed" to be built to withstand all the weird angles photograhers use them. The only reason almost everyone stores them on a lying position is we don't want bump the cabinet and cause the lens to drop from a vertical position. Also, if you have only a few lens in your collection, it sorta makes the cabinet look more filled up.
But if your cabinet is pretty full, I don't see why you can't store them standing up. I have a friend who's got about 3 cabinets all filled with stuff and he stores some of the short lens vertically.
it doesn't matter really.. but most dry cabinets come with wave foams which conform to the side of lenses so many people will store them that way... before i had my dry cabinet i used a small dry box and kept my lenses vertically coz there wasn't enough space... but the lenses are still fine...