How do single use passwords work for an encrypted message LastPass encrypts its data before sending it to their servers. The key for the data is generated using a combination of the master password and username.

How then can a one-time password be used to decrypt this data? The data on the server has been encrypted with the master password and username. Does this mean that LastPass stores a new version of encrypted data for every (single-use) password?
As hunter notes, the only people who can really say what LastPass actually does are those who work there.  However, as long as we only consider what they can and should do...

They don't really need to store a separate copy of your data for each one-time password.  Instead, all they need to store for each password is an encrypted copy of the key used to actually encrypt the data.

So, when you log in using a one-time password, the password is (presumably) passed through PBKDF2 to derive a "key-encryption key", which is then used to decrypt the actual key needed to decrypt the data.