Your Lotro software on your PC already has all the game content. There is nothing to download. Access to the content is controlled by the Turbine's accounting and Lotro server software. There is no connection between Steam's servers and Turbine's servers.
You have to retrieve the key code for the content from your Steam account. You go here:
log in with your Turbine user id and password. Apply the key code to your Lotro account.
Unless stated otherwise, all content in this post is My Personal Opinion.