"Lover to Lover" received acclaim from music critics. In a review of Ceremonials, Allison Fitts of Dart News Online praised the song, calling it "one of the most unique [songs] on Ceremonials" and saying, "'Lover to Lover' is basically what the band would have sounded like 50 years ago", and compared it to the works of Fitz & the Tantrums. American magazines Rolling Stone and Billboard, in their reviews of the album, compared the song to the work of Adele.
A music video to accompany the release of Lover to Lover was first released onto YouTube on 19 November 2012 at a total length of four minutes and twenty seconds. The video stars Welch alongside Australian actor Ben Mendelsohn and was directed by Vincent Haycock, who previously worked with the band when he directed the music video for Calvin Harris's single, "Sweet Nothing."