It seems like this is only an effect caused by Menthol and not by Menthol itself, and it also appears to only effect smokers of cigarettes and not from Menthol vapor from e-cigs.
"One potential mechanism is that menthol stimulates upper-airway cold receptors, which can increase breath-holding time, which may in turn facilitate the entrance of cigarette particulate matter into the lungs,"
There is no 'cigarette particulate matter' in e-cigs.
There are also a lot of medically orientated products on the market such as vapor rubs and
devices that produce Menthol-laced vapor to help improve breathing.