You have installed Lightroom Desktop (Currently Version 5.3) It does not support tethering. You need to install Lightroom Classic version 11.3 to get the current version which supports tethering. It has an LrC Icon instead of an Lr icon.
I downloaded LrC 11.3 now and tethering is in the list! It only doesn't connect with my camera .( It's a Nikon D800 - on my Mac it works, but not on windows. Somehow I have to solve this problem. Thank you!
I am a Windows user, so maybe I don't understand. The second screenshot shows the logo for Lightroom, NOT Lightroom Classic. Lightroom Classic is available from the same creative cloud application manager from which Lightroom is installed. It is part of the same photography plan. It has a different icon, and is installed separately from Lightroom. They are two separate and distinct Lightroom applications.