The word 'lose' is used to show that one is no longer in possession of something. You can lose hope, lose money, lose sleep and so on. 'Lose' is a verb and can be used in the past tense.
Omo, I don tire to dey type. Typing on the phone is such a herculean task! My first thread though.
'Their' in contrast shows possession, what someone owns. E.g It is their book.