This is due to the cooling of ground temperature and the reduced amount of sunlight available to the lawn.
The grasses we must grow here in Perth are warm season grasses; they thrive in the summer months with adequate watering but will go dormant in the winter. The best way to improve winter lawn colour is to promote its health and defense in autumn.
Start by lifting your mower height slightly, this will help the lawn to capture as much of that much needed sunlight as possible by increasing the size of the leaves, and give it a nice big dose of a good quality NPK fertiliser before the ground gets cold (Before the end of May).
This way your lawn will be strong and healthy and will stay a lot greener through the dormant winter period.