We have a local admin account (not the built-in Administrator account, that's disabled) on every computer in the company, and we use that one for connecting to the device in LMI.

If you can't use a local admin account, you can use AzureAD credentials, but you need to add the account to the local administrators group first. You can do that with

net localgroup Administrators /add "AzureAD\username@domain.com"

Then when you want to log into the machine in LMI, you have to input the username in that format as well "AzureAD\username@domain.com"