Exeter Chiefs flanker Ross Vintcent also comes into head coach Gonzalo Quesada's starting team for Saturday's Test in Wellington.
Italy were soundly beaten 27-10 by Japan last Saturday and now face the only top-tier rugby nation they have never beaten, losing all 18 previous matches against New Zealand.
The 33-year-old Allan will earn his 91st cap against the All Blacks, having started on the bench against Japan.
Lynagh makes his Nations Championship debut, after sitting out in Tokyo. Vintcent was on the bench for the opening match.
Benetton back-rower Giulio Marini is expected to make his debut for Italy, named as one of six forwards among the eight replacements.
New Zealand edged past France 34-32 in their Nations Championship opener, their first match under new coach Dave Rennie.
Italy team:
Starters: Tommaso Allan; Malik Faissal, Juan Ignacio Brex, Tommaso Menoncello, Louis Lynagh; Paolo Garbisi, Stephen Varney; Lorenzo Cannone, Michele Lamaro (capt), Ross Vintcent; Andrea Zambonin, Niccolo Cannone; Marco Riccioni, Tommaso Di Bartolomeo, Danilo Fischetti.
Replacements: Gianmarco Lucchesi, Mirco Spagnolo, Muhamed Hasa, Giulio Marini, Federico Ruzza, Riccardo Favretto, Alessandro Garbisi, Leonardo Marin.
New Zealand team:
Starters: 15-Damian McKenzie; 14-Will Jordan, 13-Billy Proctor, 12-Jordie Barrett, 11-Leroy Carter; 10-Ruben Love, 9-Cam Roigard; 8-Ardie Savea (capt), 7-Luke Jacobson, 6-Wallace Sititi; 5-Tupou Vaa'i, 4-Sam Darry; 3-Tyrel Lomax, 2-Codie Taylor, 1-Ethan de Groot
Replacements: 16-Samisoni Taukei'aho, 17-George Bower, 18-Pasilio Tosi, 19-Josh Lord, 20-Anton Segner, 21-Cortez Ratima, 22-Anton Lienert-Brown, 23-Josh Moorby
