I remember there being temporary lighting brought in when NU hosted the Big Ten Softball Tournament in 2014. We've hosted NCAA regionals, but I believe all the games were during the day. I don't remember an issue with hosting a super-regional, but that doesn't mean it didn't happen.
It's good question. I'm sure the neighbors would push back on there being lights and maybe NU figured they already used all their capital on the football stadium. The baseball stadium doesn't have lights either.