When we try to recreate the lists with look up columns from one site to another site, we lose the look up connection.
For example if have two sites 
A and B
A has list called A1 which has a look up column referring List AL1
If you want to take a copy of list A1 and recreate it in site B as B1 with look up referring to BL1.
Follow these steps
- Save List A1 as template (.stp).
 - Go to site collection settings.
 - open the list template gallery.
 - Save the A1's template in your computer.
 - Go to the .stp file saved in you computer.
 - change its extension to .cab
 - open the ziped file and extract the files in it to a folder.
 - Open the manifest.xml file in notepad (or any other text editor).
 - search for the GUID of list AL1 and replace it with GUID or BL1.
 - save the manifest.xml file
 - open command prompt and type the command "makecab manifest.xml template1.stp".
 - It creates the template1.stp file.
 - Upload template1.stp to the site collection of B site.
 - create the list B1 using template1.stp.
 - If you have multiple look up fields repeat the step 1 to 14 for all those fields.
 
If this is post is helpful, please leave a comment. Thanks.