Usage patterns
ライターで〈物〉に火をつけるto light something with a lighter
He lit his cigarette with a lighter.
ライターをつけるto flick on/light a lighter
He flicked on his lighter to light the way at his feet.
ライターの火が消えるfor a lighter's flame to go out
The lighter's flame went out in the strong wind.
〈人〉にライターを貸すto lend someone a lighter
I lent my friend a lighter.