Russia topped the final standings on home soil in Sochi, winning a total of 80 medals, including 30 gold, and earning the thanks of President Vladimir Putin, who lauded the "medal fireworks".
Speaking to the Paralympic Committee of Russia (RCC) Congress in Podolsk near Moscow, the 76-year-old Lukin claimed his task was to build on that success and attract some 1.3 million disabled people to sports.
"The main task is to make Paralympics sport popular," the Itar-Tass news agency quoted him as saying.
Lukin, a former Russian Ambassador to the United States, had been elected to head the RCC in 1996, 2002, 2006 and 2010.
The unanimous re-election will take Lukin through the 2018 Winter Paralympics in Pyeongchang.
Lukin had served as Russia's human rights ombudsman until February when his five-year term expired.
He claimed that up to nine per cent of the country's population had been with a disability, while less than five per cent of those people go for sports.
"We can't handle that objective ourselves," Lukin told delegates
"This is also a task of the Governors and State bodies."
The task was to double the disabled people engaged in sports, he said, admitting that would be difficult due to lack of barrier-free environment in Russia.