Plenty of people have two passports for this reason.

Lots of things in immigration require you to honestly self-report and have no mechanism to validate at the point-of-entry. For instance, many countries without visa requirements will still ask about criminal records in your native country, but have no access to the data to verify if you tell them you've never even had a parking ticket.

But if you get caught later down the line, then they are going to use your lies to make life very hard for you.