Those three meanings could be conveyed by the expression 'Drop it.'
This doesn't mean the same, but it's common when suggesting that somebody doesn't follow a line of enquiry to say 'Don't go there' or 'You don't want to know'.
A common use of 'lose it' is in the idiom 'Use it or lose it' - typically applied to a skill or habit that you need to maintain by practise: 'I used to speak good French, but now I'm a bit rusty - use it or lose it!'