Can a bad lug nut cause a vibration at 60 mph and over?

What is your question?

I replaced my front tires yesterday, on the way home it started vibrating at 60 mph, thought it was a bad balance, took it back and the tire guy broke a right front lug. Never any vibration before this, tires are less than 1 year old and have less than 100 miles on them.

What makes this problem better or worse?

It starts at a little over 60 mph

How long has your 1998 Nissan Frontier had this problem?

Immediately after having the tires replaced