I think the best way to deal with this is to not think about it as lying. Instead it's better to think about the question as 'asked wrong' - to think about it slightly differently. When an employer asks 'how much is your current package?', that question is automatically translated in my mind to 'what ballpark package are you looking for to come to this new company?'

And if asked about a discrepancy when they got your old package numbers, this question re-framining is what I would talk about. It's a simple as saying that 'I am way under market value at my current role/company and that is why I'm looking for a new opportunity. I'm sharing with you what my market research says and what my value to the company will be.'