Went to Les Schwab to install new tires. The amateurs broke one wheel stud out of 4 (see the photo below).
I need to drive 180 miles on Sunday on highways. Is it safe to do so with the broken stud?
Car: Toyota Yaris 2007, front-wheel drive. The broken stud is on the drive-side front wheel. Each lug nut requires 76 ft*lbs of torque.

While I certainly wouldn't drive it like that 180 miles on the highway, it may be okay if you crawl to your mechanic at 20mph for a few minutes.
This is a safety issue, so you never know if the remaining 3 fourteen year old studs won’t give way, from the extra stresses.
And don’t delay fixing it either.
Once it is fixed, send the bill to Les pitres and make them pay it.
I ended up having the lug stud replaced by Les Schwab without any questions and at no charge. Thanks.
Great!
no
I appreciate your comprehensive answer. Like absolutely positively no or you may drive 20mph to them to fix that?
Just put in a new stud. It's neither difficult or expensive.
Of course. I am waiting for a new stud to arrive to install it myself and I will also go to them and ask to fix their fault. It's just Sunday, and I can do neither right now. Thanks, guys.
Sorry that happened to you. A lot of places get in a hurry and either cross thread the lug nut or overtorque it. Sadly, it’s common.
But, yeah, with a 4-stud hub, there’s not much margin for error. The NASCAR guys like to say “3 points define a plane” but they’re never more than 1/2 a mile from a tow truck.
Replacing it now is the correct answer.