Well i've never heard that running nose can be related to contact lenses!!
Maybe your friend had an eye infection or an eye problem and still put on his lenses..YOu should never do that..if you have an infection never put on your lenses!!
Also maybe some dust might enter his eyes and irritate it causing his nose to run..i always have a running nose when i cry, lol!!
He should remove and clean the lenses properly!!