Yep, to lock a coin, you must burn one that you have, and in turn you create one that is locked – you must be online and communicate with the mint to do that.
Similar to sending your bitcoin into an address (that's only spendable by the receiver).
Interesting detail: the mint doesn't see what you're locking the token to, the token (and its locking script) is blinded when you do. Upon spending the coin (i.e. unlocking it), the mint sees the script it's locked to.
Soon TM we want to add zk-scripts so that the mint doesn't even see the unlocking script anymore. 2 weeks