Lungu, who is suffering from recurring achalasia, a condition caused by a narrowing of the oesophagus, was flown to South Africa on Tuesday.
He had collapsed on Sunday at an International Women's Day event in the capital Lusaka.
A team of specialists treating him said they had received "very encouraging results" and confirmed he was suffering from achalasia.
They said he would be "subjected to further examinations... after which a decision would be taken on the method of treatment."
He was initially admitted to a hospital in Lusaka after the collapse, with his office saying he was struck by malaria.
The 58-year-old newly appointed leader is being cared for by a team of four South African and three Zambian doctors at a hospital in the capital Pretoria.
Lungu won a snap election in late January following the death in office of president Michael Sata in October.
Sata was Zambia's second leader to die in office in six years, sparking calls for presidential hopefuls to undergo medical checks to guarantee their fitness.