The two teams will meet Panathinaikos and Maribor in Group J of the tournament.
"Both Tottenham and Lazio are big European clubs," Panathinaikos midfielder Pape Sow said. "The London side especially is not the best draw we could hope for. As for Maribor, I don't know them that well, but to have reached the group stage of the competition means that they are good."
Liverpool was also handed a tough draw. The three-time champions face Udinese, Young Boys and Anzhi Makhachkala, which is coached by Guus Hiddink and captained by former Inter Milan striker Samuel Eto'o.
Inter is also bidding for a fourth title and it has been handed some tricky trips after being grouped with Rubin Kazan, Partizan Belgrade and Azerbaijani team Neftchi Baku.
Defending champion Atletico Madrid is in a group with Hapoel Tel Aviv, Viktoria Plzen and Academica, while last year's runner-up Athletic Bilbao faces Lyon, Sparta Prague and Ironi Kiryat Shmona.
Marseille will meet Fenerbahce, Borussia Moenchengladbach and AEL Limassol, while Bordeaux has been grouped with FC Brugge, Newcastle and Maritimo.
"I think we're in the best group we can be," Fenerbahce vice-president Abdullah Kigili said. "Marseille and Borussia Moenchengladbach were once one of their best teams of their domestic leagues. But today they are not better than us.
"We aim to advance into the later rounds of the competition. I can even say that we set our target as winning the UEFA Europa League trophy."
Europa League debutants Levante and Genk avoided trips to far flung places. Levante will face FC Twente, Hannover and Helsingborgs, while Genk has been grouped with Sporting Lisbon, FC Basel and Videoton.
PSV Eindhoven will face Napoli in another big clash. Dnipro Dnipropetrovsk and AIK are also in Group F.
Meanwhile, top-seeded Stuttgart is grouped with FC Copenhagen, Steaua Bucharest and Molde, while Bayer Leverkusen faces Metalist, Rosenborg and Rapid Vienna.Suggest a correction