The first-leg result means Stuttgart must score at least twice in Italy to stand any chance of going through, but their away form in the competition so far gives them belief that their European campaign will not necessarily end tomorrow night.
The Swabians won 5-1 at Steaua Bucharest in a decisive group stage fixture while a 2-0 win in Genk saw them through the round of 32 after a 1-1 draw at home.
With nine goals scored on their travels opposed to just three at home, Bruno Labbadia's side have built their Europa League fortune away from their Mercedes-Benz Arena, which is why they are not going to just take in the sights in the Eternal City Thursday night.
"I would certainly not rule out us going through," said defender Georg Niedermeier.
"We go into every game to win it. The situation is certainly not ideal, but when we are on the pitch, the only thing we thing about is winning.
"We will try to make the impossible possible."
Barcelona's 4-0 win over AC Milan last night, which came after a 2-0 defeat in the first leg, will be a source of inspiration to the Bundesliga club.
"Lazio are a strong side and that reduces our chances somewhat of course, but it starts at 0-0 and if we can get the first goal, then it would become tight for them," Niedermeier added on his club's website.
Lazio will certainly not take the game lightly, even if coach Vladimir Petkovic is considering a few changes to his side after their weekend defeat to Fiorentina.
"We must not take to the field as if it is a friendly game," he said.
"We need to find the right motivation to keep our attention high.
"We must not think about the first-leg result, we saw last night that there is no such thing as a result which cannot be overturned.
"Maybe I will make some considered changes, but I have a small squad at the moment and I will pick the best team I've got."
The cautious Petkovic is not thinking about the next round, Friday's draw, or the possibility of reaching the final.
"I am just focused on tomorrow's [Thursday] game," he told a press conference. "Then, once we get through, we will see.
"We want to get as far as we can, as we do in the league and in the Coppa Italia."
Petkovic is without defender Andre Dias, who is injured along with German striker Miroslav Klose.
Stuttgart made the trip without Alexandru Maxim, who broke his nose in the first leg a week ago.
There will be no spectators inside the Stadio Olimpico as Lazio play the first of two games behind closed doors following crowd disturbances in recent home European matches.