The election on June 7 pits an alliance including Iranian- and Syrian-backed Hezbollah against an anti-Syrian coalition that currently holds a majority in the parliament.
Lavrov held talks in Beirut with Lebanon's president, prime minister and house speaker shortly after a one-day trip by U.S. Vice President Joe Biden.
"It is important that the results of these elections are recognized not only by Lebanese society but also everyone who is interested in the continued and natural development of Lebanon as a state, hence, the international community," Lavrov said.
Many pundits predict gains for Hezbollah and its allies, who include Christian leader Michel Aoun, in a tight vote that may lead to the formation of another national unity government.
"We will deal with all those chosen by the Lebanese people. We [will] respect this choice and this vote," Lavrov said through an interpreter.
Russia has been critical of Hezbollah over the past few years, but Moscow, which has traditionally enjoyed good ties with Damascus, has expressed more neutral views about Lebanese political issues than Washington.
Der Spiegel reported Saturday that an international tribunal investigating the assassination of former Lebanese Prime Minister Rafik Hariri had new information that Hezbollah was behind the killing. Hariri was killed in a Beirut bomb blast on Feb. 14, 2005.
Lavrov on Monday warned against any attempts to politicize the work of the tribunal.
"We consider what was published in Der Spiegel an attempt to politicize matters, and we consider all such attempts provocative," he said.
Lavrov signed a book of condolences at Hariri's grave on Monday.
Biden had linked U.S. aid levels for Lebanon to the outcome of the election and described Hezbollah, without mentioning the group by name, as "spoilers of peace."
"We will evaluate the shape of our assistance program based on the composition of the new government and the policies it advocates," Biden said Friday. Washington classifies Hezbollah as a terrorist group.
Meanwhile, Arab League leader Amr Moussa said Monday that he supported an initiative by Lavrov to hold talks with Islamic militant group Hamas despite strong objections by Israel.
Moussa called Israeli objections to the meetings "nonsense."
"The time has changed. Many people are sick and tired of the policies of isolation and exclusion," Moussa said on the sidelines of a financial conference in Athens.
Russia's Middle East peace partners, including the United States, insist that Hamas must recognize Israel and stop violence before it can join any international talks. But Lavrov met with the top Hamas political leader in Syria on Saturday, and Moscow has invited Hamas leaders for talks.
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