I am very thankful I found this thread. My friend and I found the "replacement iphone" process very frustrating recently. Fortunately, I'm technical. If I wasn't here to help, she would have thrown the whole thing away. We ended up having to disable/re-enable MFA in the vault account settings -> multifactor options page. The recovery email didn't work for us.
One other point on the disable/re-enable process. On re-enablement it will go to enrollment. At that point, the page will display a "protect your account" phone and backup SMS options to the user. One needs to be sure to select edit the phone to "pair a new" device to get new QR code. Without this, you're stuck in the same broken loop.
I really feel this process should be easier for the end user with direct links to clearer scenario based instructions. Considering Last Pass and Authenticator are part of the same company, it would also make sense to have an easy button in account settings multifactor options to re-pair a new phone for authenticator.