Possible lawsuit between Lorde and Bart Barker?! 

He didn't. Note that it wasn't a situation where Lorde's publishers were suing Bart; they took down his parody on YouTube using YouTube's "take down" rules where they could claim the rights to the music Bart was using and YouTube told Bart he would have to sue them to get the video back up. Given the time, effort, and money Bart had invested in creating the parody, and the fact that, in the United States, anyone has the right to parody someone else under what are called the "fair use" principles of the US Constitution (part of the amendment granting Freedom of Speech), if he had sued, he would have won. Instead of hiring a lawyer, though, he made another video explaining fair use and asking his fans to Tweet Lorde's publishers to drop their claim. That worked and the video was put back up about two days later.

It's worth noting that a similar situation happened at about the same time to a law professor at Harvard who used someone's music as the subject of a lecture he posted on YouTube about, of all things, fair use. The publisher of that music also followed YouTube's take down rules and got the video taken down. The professor filed suit and, about a month after Bart's run-in, won an undisclosed monetary award against that publisher for the time and aggravation they they cost him to even have to file such a suit. (The judge even ordered the publisher to write an apology to the professor and to write a company policy stating they would never do this again.--Don't mess with a Harvard law professor on a matter of constitutional law!) (If you want to read about it, Google "Liberation Music Will Fix Its Copyright Policies and Pay Compensation.") That may make the last time Bart or anyone else has this problem with a music publisher about a YouTube video.

Do note that fair use applies to very specific uses of copyrighted materials. Parodies and college lectures are the primary examples. Fair use does not give someone the right to use someone else's intellectual property as their own and sell it, hence the lawsuit between One Direction and Pete Townsend of The Who. Most of the songs Weird Al Yankovic has done would not qualify as parodies, so he usually pays royalties to the music publishers.