You have never lost the key! 설마 열쇠를 분실한 건 아니겠지 blow one’s chances. 기회를 날려버리다.(=기회를 잃어버리다.)

분실하다 and 잃어버리다 both mean to lose and you can use both of them for missing items. But they are a little bit different in usage. You can use 분실하다 in even formal conversation too. So, for example, you might hear an announcement on the plane, 기내에서 지갑을 분실한 분을 찾습니다. 잃어버리다 has more broad usage. You might say 아이를 잃어버리다 but we don't say 아이를 분실하다. Like 황금신 says below, you can say 기회를 잃어버리다 but 기회를 분실하다 sounds awkward. Hope this helps.

분실하다 = 잃어버리다. The same meaning.