The mayor, Central Otago councillor Gordon Stewart and Waitaki MP Jacqui Dean had "a very good meeting" with Minister for Land Information Maurice Williamson in Wellington, Mr Lepper said.
The controversial proposal to call the Hector Range peak, southeast of Lake Wakatipu, after a cooking pot has gained strength despite strong opposition. The New Zealand Geographic Board sought feedback last year on its proposal to name the peak Te Kohua after a three-legged cooking pot.
It said Ngai Tahu chief Reko guided Otago farmer Nathanael Chalmers on an expedition through the Nevis Valley in 1853 and was paid with the cooking pot. Thirty-five of 37 submissions received objected to the name but the board decided to continue with the proposal, and has referred the matter to Mr Williamson to make the final decision.
Mr Lepper and the Central Otago District Council had concerns about the appropriateness of the name and suggested an alternative - Karearea, after the native falcon.
They were also concerned about the process by which the board reached its decision, saying the council and the local community should have been consulted.
"We gave Mr Williamson a whole lot of information about the peak and I think he took us and our concerns seriously," Mr Lepper said.
"Although we have no idea what his decision will be, I'm quietly optimistic. His choices are to either accept the Te Kohua name or to reject that and consult further on a name. We're hoping he'll be doing the latter so the community gets to have an input."
Mr Williamson told them he would be in Queenstown this week and would view the peak then.
Mr Lepper, his wife Bernie and Mr Stewart climbed the 2307m peak last month.