Macmillan Cancer Support estimates cases in women will rise from about 26,000 in 2010 to 95,000 in 2040.
Cases in men will increase from 39,000 to 42,000.
Macmillan warn that lung cancer gets just a quarter of the research funding given to breast cancer.
Lung cancer kills more people in the UK than any other cancer. Cases of lung cancer reflect smoking rates two to three decades earlier, and about 80% of cases are linked to tobacco.
The peak time for smoking in women was in the 1960s - 20 years after the peak in male smoking.
And while cases in women will far exceed those in men, the charity says that by 2040 fewer than half (47%) of women with lung cancer will be alive at least five years from diagnosis compared with three-fifths (59%) of men.
An analysis by King's College London for Macmillan suggests there will be an overall doubling of lung cancer cases from 65,000 in 2010 to 137,000 in 2040.
It says this will largely be due to an ageing population.
Ciaran Devane, chief executive of Macmillan Cancer Support, said: "Lung cancer is often overlooked among cancers but these figures should serve as a firm reminder that it is still very much a cancer killer.
"For most cancers in the UK we are looking at how we can cope with a population of long-term survivors with health complications.
"With lung cancer we are a long way from even being able to consider these issues."
He said research was a key part of improving lung cancer outcomes, and added: "It is nonsensical that research in this area receives such minimal funding compared with other cancers. This has to change."
The number of women living with lung cancer in the UK is set to rise significantly faster than the number of men with the disease over the next 30 years, experts say.