Mr Lavrov met Iranian foreign minister Mohammad Javad Zarif and Turkish foreign minister Mevlut Cavusoglu.
Zarif also stressed that cooperation between Russian, Iran and Turkey in the Astana process was producing results. "The Astana process is being promoted by all participating countries".
The presidents of Iran, Russia and Turkey on April 4 reaffirmed their commitment to work toward achieving a sustainable ceasefire between the warring sides in Syria and bringing peace and stability to the war-torn Arab country.
On Lavrov's stance on preconditions, Al-Aridi said: "Does this mean that the opposition or Syrians in general should be completely submissive to Russian and regime's dictatorship?"
One week after the incident, the US, Britain and France launched a coordinated missile attack against sites and research facilities near Damascus and Homs with the purported goal of paralyzing the Syrian government's capability to produce chemicals. Both Russia and Iran have deployed forces to Syria to back up Assad against anti-regime fighters.
Alexander Shumilin, a Middle East expert at the Institute for United States and Canadian Studies in Moscow, however, said the Douma fallout had "caused a crack in the alliance of three countries".
"What is important to understand is that the Russians, they are very pragmatic players", said Lieberman during a discussion on the alliance between Russia, Syria and Iran at the Washington Institute for Near East Policy.
Al-Aridi said: "We have to ask ourselves, is the Assad regime's brutality helping the peace process; are Russian strikes, the regime's bombardment, displacement of Syrian civilians and Moscow's cover-up of the regime's crimes helping the peace process?"
The next Syria talks in Astana are set for May 14.
Putin hosted a summit on Syria with the Iranian and Turkish presidents in November.