As a Platform Manager, you can grant access to create lists by either Role or by individual User.

By Role

Platform managers always have access to build advanced lists. To give other roles access:
  1. ​Navigate to Core > Lists > More Lists.
  2. Select List Admin at the top.
  3. Click Access in the top right and select ​Advanced Role Access​.
  4. Check the box next to each role you are granting access to.
  5. Click ​Save & Exit​.
 

By User

To an individual user(s) access to create advanced lists:
  1. ​Navigate to Core > Dashboard.
  2. On the Lists block, click View All.
  3. Select List Admin at the top.
  4. Click Access in the top right and select ​Advanced User Access.
  5. Use the search tool to find the user you want to add.
  6. Click the blue >> next to a user's name to move them from Search Results Column to Added Users.
  7. Click Save & Exit.