On multisite setup, currentUser not true in LivePreview
I have found the solution to my problem.

{% if craft.app.request.isPreview %}
    THIS WILL BE SHOWN IN LIVE PREVIEW,
    even if Your domains are
    www.main-cp-domain.com
    www.second-domain.com
{% else %}
   THIS WILL APPEAR TO ANYONE ON FRONTED
{% endif %}


So it does what I need. However, I don't get why craft.app.request.isLivePreview and currentUser are not working in LivePreview, when editing entries for second-domain.com