"If ALNM did not close last week, would N2N have chosen it instead?"
I don't think when A Little Night Music closed had any influence on when Next to Normal closed. Many a time have multiple shows closed on the same day.
A lot of factors go into determining when a show should close. Often shows may decide to close at the end of leads' contracts. If the show didn't recoup yet, it may also be a money issue; financially would it make sense to keep the show running for another week or two? Finally, timing is also a factor. A show may be doing well in the present, but do advance sales look great after a major holiday? This is why a lot of shows close in January right after the holiday season.
"We like to snark around here. Sometimes we actually talk about theater...but we try not to let that get in our way." - dramamama611