Hello @at.witke
Thank you for the post.
Per checking your account, we could see you have a Free LastPass account. This means you have one type of device that can be used, in this case, it is a desktop. Therefore, you may access the vault from the web as many times you want, however, the access to the mobile app may be restricted, as you would need to switch, and these are limited; and the list of Mobile Devices will be empty.
Related to the two-factor authentication of the account, this is a process that connects the account with the authenticator app in the device. If this is the app you are describing, it is expected the code will prompt only on the device that has synchronization.
Thank you,
Karol | Customer Care