An example of my regular extreme condition is snowboarding off piste near the top of Whistler during January. I've read that a butane lighter is bad at high altitudes. I'll get one just to test it out, but I won't make it part of my big three...yet.
Whistler is 7100 feet in elevation. I know from personal experience that BIC type lighters work at that height. The highest elevation I ever used a BIC was at 7800 feet.
At that elevation, the BIC lighter and then my pocket rocket stove worked good enough to cook dinner for 4 people.
In winter, when the temperature drops below about -10C (14F) , any butane lighter or fuel cannister will work as long as it kept warm in in an inside coat pocket before using. The stove's fuel cannister benefits from a small fleece cover that keeps it somewhat resistant to the cold until the food is cooked.