was it ever performed on stage?
Yes, in Berlin .
Up Where We Belong
In 2013, Cocker was honored in Berlin with a Goldene Kamera award, and Warnes joined him to sing the song at the ceremony.
who sings the song love lift us up where we belong Joe Cocker and Jennifer Warnes . what is the theme of this song? The  struggles of life and love and the obstacles in the way that we attempt to dodge.
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Up Where We Belong [SEP] Live performances
Warnes and Cocker kept to an agreement that they would never lip-sync their performances of the song. One of their earliest live appearances was on the November 20, 1982, episode of "Solid Gold". "Saturday Night Live" followed on February 5, 1983, and their performance at the 25th Annual Grammy Awards came later that month, on February 23. Backstage at the Grammys Warnes said about working with Cocker, "I was told it was the weirdest pairing ever," and regarding their April 11 appearance at the 55th Academy Awards, she admitted, "Neither of us were comfortable in the Oscar world. Joe performing in a white tuxedo, me in pink taffeta—how absurd." In 2013, Cocker was honored in Berlin with a Goldene Kamera award, and Warnes joined him to sing the song at the ceremony.