Short answers, pulled from the story.
Valla proved that the Donation of Constantine was a forgery, not a genuine 4th-century document. He showed through linguistic analysis that the document's Latin style dated to the 8th century, noted that it used the word "satrap" which Romans of Constantine's era would not have used, and pointed to the absence of any contemporary evidence for such a vast transfer of power.
Valla wrote the essay between 1439 and 1440 while employed at the court of Alfonso V of Aragon. The work was not formally published until 1517, more than seventy years after it was written.
Valla was put on trial before the Catholic Inquisition in 1444, most likely because of his essay attacking the Donation of Constantine, which undermined the legal basis for papal territorial authority. Alfonso V of Aragon, who was in a territorial conflict with the Papal States at the time, intervened to protect Valla from imprisonment.
Erasmus stated in his De ratione studii that for Latin grammar, there was "no better guide than Lorenzo Valla." Erasmus also found Valla's notes on the New Testament, the Adnotationes in Novum Testamentum, in Leuven in 1504 and published them in 1505.
Valla's De Elegantiis Latinae Linguae was reprinted nearly sixty times between 1471 and 1536. Richard Claverhouse Jebb described the work as marking the highest level yet reached in the critical study of Latin.
Valla was originally buried beneath the bronze Lex de imperio Vespasiani behind the altar of Saint John Lateran. His tomb and epitaph were last recorded by Seyfried Rybisch in 1570. In 1576, Pope Gregory XIII had the tomb destroyed when he removed the bronze to the Palazzo dei Conservatori. A memorial to Valla now stands in the Lateran in its place.