In LeanKit, only users who are Account Administrators, or users to whom the Board Creator right has been given, are able to create new boards. To make a user an Account Administrator, see the instructions here.
To grant a user the ability to create boards without making them an administrator, you can grant them Board Creator rights.
Click the Account Settings icon in the top bar.
From the Account User List tab, click the three dots to open the hamburger menu and select Edit.
Then from the Account Role dropdown, select the Board Creator role. Click Save User when you’re done.