How the lug nut is tightened is very important. Too tight and too tight can cause problems. So, yes, it's not good to over tighten the lug nut. Excessively tightened lug nuts can peel threads, damage wheels, damage brake discs, and may clip wheel bolts. However, insufficient tightening of lug nuts can cause them to become loose, with disastrous results.

Therefore, do not screw the lug nut too tight or too tight. Make sure you know exactly how much torque they require. Or, if in doubt, consult a certified professional for help in installing or tightening them for you.