Shortly before the results became known, Assange posted a message on his Twitter account, asking Lasso to flee the country.
"I cordially invite Lasso to leave Ecuador within 30 days (with or without his tax haven millions)," he wrote, alluding to claims that the conservative banker has money stashed abroad.
The candidate for the ruling PAIS Alliance, Lenín Moreno, is the apparent winner of Sunday's runoff.
In one of them, the US ambassador to Ecuador, Linda Jewell, wrote: "Moreno conveys a mature, serene demeanour and a genuine commitment to making a positive difference for his country.
"While not one of Correa's top political advisers, he seems to enjoy good access and to have developed the President's respect.
"We expect him to be a moderating influence on the administration. He will be a useful partner and advocate for many of our development assistance programmes, and he will likely also be a useful and strategic conduit for political messages that may be difficult to deliver directly to Correa."