The Maribor goalkeeper, whose younger cousin Samir plays between the sticks for Inter Milan, spent three years with Mantova before joining Empoli for the 2010-11 season.
Now back in his homeland, Handanovic has helped his team-mates open their 10th domestic title defence with five consecutive victories.
And the Violets are also plotting to build on last year's maiden Europa League adventure, in which they failed to progress from the group stages.
"We are giving our all in every game but this task is particularly challenging," Handanovic told Maribor's official website. "Lazio are a very good team.
"Before leaving the stadium on Sunday I managed to stream their game against Siena and, despite leaving Hernanes, (Mauro) Zarate and (Libor) Kozak on the bench, they won.
"Lazio are a good side both tactically and physically so we have to get at them from the start. We can't afford to wait."
Maribor lost 4-0 both home and away to Sven-Goran Eriksson's Lazio during the 1999-2000 Champions League group stages, but Handanovic feels the Slovenians are a much-improved prospect these days.
He added: "We are growing in confidence thanks to our excellent results and we aspire to get even better.
"We are possibly playing out of our skins a little bit but let's see if we can make the most of that in Rome."
Lazio boss Vladimir Petkovic finds himself fighting on two fronts as the Biancocelesti try to consolidate a strong start to the Serie A season.
The Bosnian coach told Gazzetta.it: "We have to approach Europe in the same way as league games.
"Getting your head straight counts for a lot, in every game there are tricky moments that you have to deal with.
"Maribor have been one of the very best Slovenian sides over recent years, so we have to be careful.
"They showed what they are capable of against Panathinaikos, they have quality young players and today we will watch a video of them in action."