The Italians have not won since beating Catania 3-1 on September 25.
Sunday's 2-1 defeat at Atalanta dropped Lazio to ninth in Serie A and piled further pressure on head coach Vladimir Petkovic.
Lazio striker Brayan Perea told Gazzetta dello Sport: "We are playing as the coach tells us to, but right now results are not going our way.
"We are going through a difficult time but I'm sure that we will overcome this with hard work."
Perea, who scored his first Serie A goal at the weekend, is set to partner Miroslav Klose in Lazio's attack as the Rome club look to remain unbeaten in Europe.
The Italians are level on four points with Trabzonspor at the top of the pool and ahead of the Turkish outfit on goal difference.
Opponents Apollon bounced back from their 2-1 defeat to Trabzonspor with a 1-0 victory at Legia Warsaw earlier this month.
Gaston Sangoy's goal allowed the Cypriots to climb to third place, one point adrift of Lazio.
Apollon coach Christakis Christoforou is aware his team faces another huge test against their Serie A visitors.
"Of course the victory at Legia has pleased us and it's a big success for us," Christoforou told www.apollon.com. "But we cannot forget that we haven't done anything yet.
"We know that Legia and Lazio are superior teams to us."
Apollon warmed up for the game in Nicosia with a 4-0 triumph over AEK Kouklia on Saturday.
They remain level on 15 points at the top of the Cypriot First Division with Anorthosis Famagusta and Ermis Aradippou.
Lazio welcome back defender Stefan Radu from injury while midfielders Senad Lulic and Antonio Candreva have remained in Rome to recover from their respective muscular problems.