You should be able to update the LastPass account email without access to the previous email account, as long as you can log in to your LastPass account and access your account settings. Here's the steps to update your LastPass account email: https://support.logmeininc.com/lastpass/help/how-do-i-change-my-email-address-for-lastpass
No joy...tried all that, and the dialog box for accepting a code never showed. I think the request to set a code is being sent to the deleted email account. Only message I get at the new email address is a message verification.
So that we can investigate and so that you don't post any private account information publicly, could you send me a private message with your LastPass account email address? To send me a private message, please click my username to view my profile, then click the blue "Send a Message" button in the upper right.