I have a list (A) that I want to copy data from several columns onto list (B). However, when I use the Lookup as the column type, not all columns are available from list (A). I've never had this issue in the past when linking multiple lists.
Lookup columns can only only be "Single line of text", "Number" and "Date and Time". If your missing columns are unsupported then that would explain the issue you are experiencing.
More information located here: https://support.office.com/en-us/article/Create-list-relationships-by-using-unique-and-lookup-column...
I hope this helps.