The Lost Road was the unfinished time-travel novel J.R.R. Tolkien began as a companion project to C.S. Lewis’s The Dark Tower.
Tolkien and Lewis exchanged ideas for stories involving time travel and began separate projects in the 1930s. Tolkien’s The Lost Road was intended to connect different historical periods through recurring father-and-son figures. Its planned episodes included modern England, the sinking of Númenor, and earlier stages of human history.
Tolkien abandoned the project before completing it. Material from the work was later published in The Lost Road and Other Writings, the fifth volume of Christopher Tolkien’s History of Middle-earth series. The surviving text is valuable because it shows how the Númenórean legend developed before its later form in The Lord of the Rings and The Silmarillion.
The Notion Club Papers is another unfinished time-travel-related Tolkien work, but it belongs to a later period. The question identifies The Lost Road because it was the project directly associated with Lewis’s The Dark Tower.