A failed electronic control board, bad user interface control, broken light switch, bad light bulb sockets or a wiring failure can prevent the lights from working.
Unplug the range hood and check the wire harness connections between the light sockets and the control board or light switch. Reconnect any loose wires and repair any broken wires. If the wiring is okay, check the electronic control board for burn marks. Replace the control board if you see burn marks because the burn marks indicate a control board failure.
If your range hood uses a user interface control to control the lights, you may need to replace the user interface if it isn't sending signals to the electronic control board when you press user interface buttons. A user interface control is a keypad and display panel that sends signals to the electronic control board through a ribbon wire cable when you press its selection buttons. DIY testing of the user interface control isn't available for most range hood models. If the electronic control board doesn't activate the lights, you'll likely need to replace the electronic control board. If the lights still don't work after replacing the control board, you'll likely need to replace the user interface control.
If your range hood uses a switch to control the lights, unplug the range hood and test the switch for continuity using a multimeter to see if the switch allows current to flow to the lights when you turn the switch on. Replace the switch if you don't measure continuity through the switch when it's turned on.
With new light bulbs installed and the range hood unplugged, check for continuity through the light sockets with new light bulbs installed. Replace the sockets if you don't measure continuity through the sockets with new bulbs installed.