Encryption is deterministic, given an input and key, it will always decrypt. There is no way to involve a random number sent over text in the process. Further decryption isn't really authenticating the decryptor, so the acronym doesn't really fit. The user's MFA has no bearing on an offline attack against the encrypted stores.
how does one mitigate the effects of the LastPass leak
There is something to take from MFA. Remember the multiple factors know, have and are. If an attacker can exfiltrate ("know") both the encrypted data and the key, it's game over. If the key can be turned into something one has it's a lot stronger. This is what we do with HSMs. These have strong assurances that private portions of key material can never leave the HSM. One has to "have" the HSM (or more accurately have access to the HSM) to decrypt anything. Given an HSM is standard practice for most cloud based storage of PII hopefully LastPass did this and these encrypted backups will stand the test of time.
Final pedantry:
One could simply attack the crypto involved, bypassing the need to "have" the HSM involved. But this is probably akin to guessing what code the user was sent over SMS. Not impossible, but improbable on the scale of a useful attack.