(to) lose = 失う 失せる is more like slang. eg: 失せろ = get lost!, get out of my sight, piss off....etc

The most common word for "to lose something" is 「・・・を　なくす」. e.g) かぎをなくして家に入れません。 I lost the key and cannot get in the home.

失うis the word for "to lose," as in to lose a physical object. 失せるis a closely related word, but it means to disappear or vanish.

Both common

As you can see Word in Dictionary “失う”　＝(some reason you can found)　Ｌｏｓｔ　in use I lost a Book (Watashiwa hon wo ushinasu" is common " 失せる”　=(disappear or out of sight )Lost I will disappear form the here (Watashiwa kokokara useroyou) or The diamend has disappeared from the safe. (Diamond ha kinko kara useta)