Beck has recorded a song with Lady Gaga for her upcoming 2016/2017 album. (No specifics have been announced.) [Update: Beck's song on the album is apparently "Dancin' In Circles".]
Lady Gaga has been very vocal about her Beck fandom. After Beck's big Grammys win, she mentioned numerous times how much she loved him, and even told a story about going to see him at Bonnaroo before she was famous (in 2006). Once she even Snapchatted a picture of her kissing a framed picture of Beck on a studio's wall.
Anyway, Beck was at a fashion show and Lady Gaga and her new album's producer Mark Ronson were there. This seems to have led to him getting to know Gaga. Gaga explained they were hanging out and just "shooting the breeze" in Malibu, and she asked him what he was doing for the rest of the night. She invited him to jam, and it led to a "great dance song."
A year or so later, Beck said about his work with her: "I just came in and threw a bunch of ideas together. The thing we did felt like late 60s Stones, Fleetwood Mac, Stevie Nicks. Acoustic and a bit gritty." He then reminisced - "we had a whole day singing, drinking and smoking, then she made this huge Italian feast. All the while she is in ten-inch heels! I don't know if I've met anyone quite like her."