Permission Violation - Create Task from Custom Record after Submit

I have a custom record type setup with an online form which collects lead information. I have a User Event script on the custom record which creates a lead record and contact record after Submit. This all works fine both on the internal Netsuite form and the external online form.

I've written the script to create a task also, however when a custom record is created from the online form the following error is thrown, and the task is not created:

Permission Violation: You need the 'Lists -> Tasks' permission to access this page.

I am assuming that this is because the online form user role does not have the appropriate permission, is there any way I can add this permission to that role or is there a workaround?