No further information about the group is known or how many farmers it represents.
All inquiries to the group are directed to its Queenstown-based lawyer Michael Walker.
Between the start of May and the middle of September, the level of the lake was below 340m, falling to 338.5m in July.
Yesterday, it had climbed to 340.55m.
Traditionally, spring was when the lake was at its lowest, but the farmers were concerned as the lake was already at an historically low level and the impact on the water table was being observed.
There had been reports residential water bores in the Hawea Flat area were significantly lower than in previous years and were drying out.
Farmers were concerned when they started irrigating their land in the coming months they would be blamed for any water shortages.
There needed to be a more scientific and forensic understanding of the water supply and how the level of the lake affected it, the group said.
Contact Energy's head of hydro generation Boyd Brinsdon said this was the first time Contact had been made aware of the group's concerns but would welcome the opportunity to sit down and talk to them.
Autumn was particularly dry this year, which meant the inflows into the lake were at their lowest level in about 80 years.
Because of the historically low lake levels, Contact produced more energy from its Taranaki gas-fired stations, Mr Brinsdon said.
''We're always keen to talk to community about our sustainable approach to operating on the Clutha and regularly talk to local groups who get in touch.''
Monitoring of Hawea Flat bores by the Otago Regional Council showed a slight decline in water levels from July 2014 to September this year.