I would like to quote a few lines of a lyric from St. Vincent's song "New York", for an 'in memoriam' I want to put in a newspaper on the anniversary day of my friend's death. Do I need to get permission for this? (i'm in new York, the paper is in massacusetts)
Ask the newspaper. They will know this stuff backwards and forwards.
If you put the lyrics into a program to hand out at a memorial service or other event, you're good.
If you put the lyrics (well credited) on your personal blog, and you're only quoting a small percentage, you're almost certainly fine. Given the context, it's unlikely that anyone will hassle you or do more than ask you to remove them (and even that's unlikely).
Publishing in print (or in a commercial online location) is a whole other can of worms. While the standards aren't legally stricter here, you're more likely to come to the attention of people who care.
There is no perfect formula for what's allowed and not allowed. Your memorial statement may not even qualify as Fair Use, but given the context and non-commercial nature, you're maybe okay there.
Writer's Digest has many suggestions for navigating this.
Fair Use is:
...For purposes such as criticism, comment, news reporting, teaching …, scholarship, or research...
The main issue I see is how much of the work you're quoting:
Quote or closely paraphrase as little as possible to make your point: under 10% is best; above 20% is high risk (though a recent case allowed that, where mainly facts were copied).
Unless you are able to get permission directly from the copyright holder of the song, asking the newspaper is truly your best bet. They have dealt with this before. They know what needs permission and what doesn't. They know how to get permission if needed. And they will recommend editing to acceptable levels of quotation if that is required.