Ousted president Zelaya insists voter turnout was low and calls vote illegitimate.
He has repeatedly denied this and pointed out that it would have been impossible to change the constitution before his term in office was complete.
Divisions in the Central American nation remain wide after the weekend election held by the de facto government that had removed Zelaya. Zelaya’s supporters had boycotted the vote.
Lobo, who was defeated by Zelaya in the 2005 election, has pledged to form a unity government and seek dialogue.
He is due to take office on January 27, when Zelaya’s term officially ends.
The de facto government hailed the elections as a broad success, but Zelaya’s camp called for them to be cancelled and accused election officials of inflating participation figures.
The United States and the European Union said they saw the polls as an important first step forward.
But other nations in Latin America, including regional power Brazil, said they served to whitewash the coup.