I had to create a Content Type in the Content Type Hub which has a Lookup column... I created the list of the lookup in the CTHub and published the CT. In my site collections I can see the new CT but i cannot see the lookup column... Why?
Lookup columns will only lookup data in lists in the same site/web. When the content type hub functionality deploys your content type to other sites, the lookup list does not exist there, so the column is removed.
The best way to do this is to use a managed metadata term set instead. The term set is globally available to all site collections. So you can add a managed metadata column to your content type, giving lookup type functionality, and the column can work in any site collection.
Alternatively, you can provision your lookup column with a feature receiver everytime you create a new website. You just need to make sure you have the lookup list available somewhere (which, by the way, CAN BE in a different web site). There is a quick and easy to implement guide which you can find here: http://sharepointbitsandbytes.com/2015/05/configure-lookup-fields-programmatically/ . This requires a bit of SharePoint knowledge, including features, receivers etc.