You don't need a LOI anymore. That is part of the tricky stuff about AZ. The rules change constantly and some websites are old with dated info, like any that say you can get the visa at the airport. No more.

What you need instead of the LOI is a stamped, certified letter from your hotel with all the details of your reservation on it. If you deal with an agency or the embassy, you have to paper copy it (JW Marriot sends it as an email attachment, not thru snail mail) and attach it to your application. We now have that. It is not satisfactory just to use your Marriott reservation info. We had to get the email address of the Baku Marriott to request this doc. We called Marriott to get the email address. If you are using the e-visa program with an approved vendor IN AZ, you just email the attachment to them. That part we got right so far!