The only people who can answer your question definitively are the programmers at LastPass, however, I'll try.
I assume you're referring to this. If LastPass really does encrypt your data with your password/username, then logically it could only be decrypted with the same key.
Their 'one-time' password feature is an interesting idea, but I'm dubious about it. They use 256-bit AES to encrypt your data - this is symmetrical encryption, which means that there's only one single key used for encryption/decryption.
In answer to your question, yes - it would make sense that they would have to create/store a copy of your data, encrypted with the 'one-time' password, for each one-time password that you create.
The only way (that I can think of) to avoid making a separate copy of your data for each 'one-time' password is if there is a server-side 'back-door' into your account, which would put your data at extreme risk (but I doubt this is the case).