Temae Baeri, who lives on south Pentecost, described the damage as more serious than the destruction left by Tropical Cyclone Harold in 2020.
He said a landslide on a new tarsealed road was making it hard to travel between north, central and south Pentecost.
The cyclone has been downgraded to a tropical low in the latest weather information from the Vanuatu Meteorology and Geo-hazards Department.
Vanuatu's National Disaster Management Office (NDMO) was expected to deploy staff on Thursday to the provinces hard hit by the storm.
Staff will assess the damage and find out what people on the ground need urgently.
RNZ Pacific correspondent Hilaire Bule said due to the destruction of the telecommunications network it was hard for the NDMO to collect damage reports on affected islands.
Government chief information officer Gerard Metsan said the government's telecommunication networks in the northern part of Vanuatu were down.
Vodafone and Digicel were trying to restore their networks.
The management of Vodafone said they were negotiating to fly in a helicopter on Thursday to carry out an aerial assessment of damage to their network.
World Vision Vanuatu director Kendra Derousseau said Port Vila got heavy rain overnight.
In Torba and Sanma provinces, gardens and some households were destroyed, "but we know that the central provinces of Vanuatu - Penama and Malampa were the most affected", she told Morning Report.
She said it was the result of strong winds from Tropical Cyclone Lola that entered the archipelago as a very strong category 4, and made direct landfall on the island of Pentecost which in 2020 had been devastated by category 5 Tropical Cyclone Herald.
"People on the island were still rebuilding, given the extent of the damage in 2020, and that recovery had not yet been completed when TC Lola came through."
She said spotty communications on Pentecost and into the islands of Ambrym and Malekula in the Malampa province "report major household destruction, complete livelihoods, and agricultural destruction as well as contaminated water sources and major infrastructural issues with all schools".
"At this stage, there are no reports of loss of life or injury, noting that Vanuatu is very resilient and given that there was excellent ahead of warning, people knew to get to evacuation centres and shelters, and unfortunately Vanuatu has plenty of experience with large cyclones having been battered by the twin Cyclones Judy and Kevin in March of this year.
"So people knew what to do to protect themselves and their families."
Derousseau said food security would be a major issue post-cyclone.
"We do anticipate international support being necessary."