Striker Lebedenko, 29, who leads the Chechen club in scoring this season with six goals in 19 games, has received his first international call-up.
Ivanov, 26, has been called up for the first time since 2008 when he was part of Russia's Euro 2008 squad under coach Guus Hiddink but never played in the tournament.
Capello also included strikers Maxim Grigoryev and Fyodor Smolov, who only made their international debuts in November's friendly against the United States, in his 26-man squad for the Iceland friendly in the Spanish resort of Marbella on February 6.
However, Arsenal forward Andrei Arshavin and Reading striker Pavel Pogrebnyak again were left out by former England manager Capello, who replaced Dick Advocaat following Russia's poor showing at Euro 2012.
The Russians have made a flying start in their 2014 World Cup qualifying campaign under Capello, winning all four of their matches in Group F. They next visit Northern Ireland in March.
Goalkeepers: Igor Akinfeyev (CSKA Moscow), Anton Shunin (Dynamo Moscow), Vladimir Gabulov (Anzhi Makhachkala)
Defenders: Alexander Anyukov (Zenit St Petersburg), Alexei Berezutsky (CSKA Moscow), Vasily Berezutsky (CSKA Moscow), Sergei Ignashevich (CSKA Moscow), Kirill Nababkin (CSKA Moscow), Andrei Yeshchenko (Anzhi Makhachkala), Vladimir Granat (Dynamo Moscow)
Midfielders: Igor Denisov (Zenit St Petersburg), Roman Shirokov (Zenit St Petersburg), Vladimir Bystrov (Zenit St Petersburg), Viktor Faizulin (Zenit St Petersburg), Alan Dzagoyev (CSKA Moscow), Denis Glushakov (Lokomotiv Moscow), Alexander Samedov (Lokomotiv Moscow), Dmitry Kombarov (Spartak Moscow), Yuri Zhirkov (Anzhi Makhachkala), Oleg Ivanov (Terek Grozny), Alexander Ryazantsev (Rubin Kazan)
Forwards: Alexander Kerzhakov (Zenit St Petersburg), Alexander Kokorin (Dynamo Moscow), Fyodor Smolov (Anzhi Makhachkala), Igor Lebedenko (Terek Grozny), Maxim Grigoryev (Lokomotiv Moscow)