Lighters and matches on a plane
Ordinary and torch lighters
For a US flight, FAA allows one ordinary butane or absorbed-liquid lighter per passenger in carry-on or on your person. Keep it out of checked baggage, and remove it if your carry-on is checked at the gate. A torch or jet-flame lighter is prohibited in both bags. The FAA lighter rules distinguish the flame types; a cap does not turn a torch lighter into an ordinary one.
Electric lighters and fuel
A lithium-powered electric lighter belongs in carry-on, protected against accidental activation. FAA prohibits charging it during the flight. Lighter fuel and refill canisters are separate forbidden items; see the fuel and camp stove guide before packing related equipment. A gun-shaped lighter is a separate TSA screening case, not covered by the ordinary-lighter allowance.
Safety matches have their own limit
FAA permits one book or packet of safety matches in carry-on or on your person. Take it out if the bag will be gate-checked. Strike-anywhere matches are forbidden in carry-on and checked baggage. Read the FAA match rules for the distinction, and check a different departure country's rules for the return journey.