Answer
Lightning Payroll lets you assign a Fair Work award and classification to each employee. This information appears on their payslips and helps you select the correct pay rates when processing a pay run. Before assigning an award to an employee, make sure you have already created the award under Company >> Awards and set up the relevant classifications and pay rates under Company >> Pay Rate Groups. See How Can I Set Up Awards, Classifications or Pay Rate Groups? for that step.
In the Desktop App
Open Employees >> Pay Settings and select the Pay Rates tab. Use the Award dropdown to select the award the employee works under. The Classification (Award) dropdown then shows the classifications available for that award. Select the employee's classification.
Once an award and classification are selected, use the Base Ordinary Rate field to optionally set the employee's ordinary rate from one of the pay rates imported under that classification. If you leave this blank, the employee's ordinary rate defaults to the value in the Pay Rate Per Hour field above.
In the Online (Web/Mobile) App
Open Employees >> Pay Settings for the employee. The Award and Classification fields are available on this screen (Australian companies only). Select the relevant award from the Award dropdown, then choose the employee's Classification. You can also set the Award Hours Per Week and Base Ordinary Rate (Requires company pay rates) if applicable.

Once saved, the employee's award and classification name will appear on their payslips, and any pay rates defined under that classification will be available to select when processing their pays.