The worry isn't that they'll call the cops. They'll sack you. You won't have references for the position. If you put it in your resume they may call up and find out when you apply for a new position, which would sink you. If you leave it off, you're missing out on possibly better paying jobs that would have hired you if they knew about all your experience. It's likely to make things difficult for you down the line.

But yeah you can absolutely lie... Just be aware that if you're trying to build a career it's likely to be more counterproductive than not. Otherwise, go for your life!