Did Jesus die for our sins? I don't get this part.

Did Jesus die for our sins so that we could sin as much as we want to?

And if so, why is it a sin to eg. lie, steal, cheat, if Jesus already died for us so that we could sin?
No, Jesus did not save us so we can sin as much as we want to.  In fact, the actual consequences of sin are temporary pleasures and lasting pain.  Why, then, would Jesus want us to incur greater amounts of lasting pain?  Sin is always to our loss, perhaps not always physically, but we are not merely physical beings.  We are spiritual beings, so the spiritual consequences of sin are always to our loss.
The epistles are mostly instructions for holy living, and holy living is what we are saved to.  We are saved from sin and its penalty, but we are also saved to something.

For God has not called us for the purpose of impurity, but in sanctification.  1 Thessalonians 4:7 NASB
But like the Holy One who called you, be holy yourselves also in all your behavior  1 Peter 1:15 NASB

So, the assumption that sin is actually good is invalid.