Please follow the below steps to provide permission to a specific folder in Mac.
> Navigate to the export folder location as provided in the export menu.
> Make a CTRL + Click on the folder and then choose Get Info
> Expand Sharing and Permission.
> Please click on the Lock.
> It will ask you to type in the password to Unlock it.
> Click on the drop-down list in front of the respective your user name and select Read & Write.
> You may also change the permission for Everyone.
> Once done, Please click on the Gear icon and Then select Apply to enclosed items
> Restart Lightroom and try to export it now.
For more information on How to set permission, please follow the below link.
OS X Yosemite: Set permissions for items on your Mac
Please let us know if this helps.
~Mrinmay