Neither team was able to break the deadlock during the 90 minutes at Lazio's home ground, the Stadio Olimpico in Rome.
In another Group E match, Marseille beat Lokomotiv Moscow 1-0 with a goal from Arkadiusz Milik at the Stade de Marseille.
Galatasaray top Group E with 12 points, while Lazio are in second place with nine points.
Lazio moved to the Europa League playoff round while third-place Marseille qualified for the Europa Conference League knockout stage.
Confirmed in the round of 16 (group winners)
Olympique Lyon, Monaco, Spartak Moscow, Eintracht Frankfurt, Galatasaray, FK Crvena zvezda, Bayer Leverkusen and West Ham United.
Confirmed in knockout playoffs (group runners-up and Champions League third-place finishers)
Rangers, Real Sociedad, Napoli, Olympiacos, Lazio, Braga, Real Betis, Dinamo Zagreb, Barcelona, Borussia Dortmund, Leipzig, Porto, Sevilla, Sheriff, Zenit, Atalanta.
