You're not obligated to make the lock unlockable for them, though.
The government can probably break many consumer-grade encryption schemes if they so choose to as well, but much like having to break in to your house through your locks instead of merely unlocking them, it raises the cost of law-enforcement doing so, and incentivizes them to make more restrained choices (eg, not taking literally everything they can get their hands on).
They can ask. A court order to reveal your password is enough. If you don't comply you usually run into troubles. This Wikipedia page http://en.wikipedia.org/wiki/Key_disclosure_law explains how it works in some countries.
Well... there's no real need to say that, because it's already the case. If they want to open your locks, they will.