LastPass double-hashes (ignoring iterations) master passwords. It has a client component based on PBKDF2 and a server component (per this article) also PBKDF2 based.
If the bad guys stole the hashes after they were hashed by LastPass's servers then changing the client iterations wouldn't do a damn thing. However because LastPass have an unknown network compromise one could worry that the bad guys intercepted LastPass client-hashed passwords between the client and server.
IF they modified the LastPass client, they could have it send LastPass's servers the already client-hashed password and therefore login even without knowing someone's plain text master password.
By altering your account iterations even by 1, you've now effectively forced them to decrypt the client hash (to plain text) before they could use it to login to LastPass's servers.
Again this only helps if they intercepted network traffic on LastPass's internal network.
PS - The OTP thing is as you said.
PPS - A better idea is just to change your master password.