The installation guide asks to make sure the user identity associated with application pool running SPLMS web application have farm admin rights. Where can we check this?

You can check this step using either way:
1. In the IIS configuration -  application pool, identity settings.
2. In CA you can look up what account is used for the webapplication through Service accounts.
Then you should ensure that this account is included in the farm administrators group. And if not - you should add it there, and reload SharePoint services and  IIS.