Large eucalyptus tree – exposed roots and lawn

Hi all,

I’ve got a large established eucalyptus tree on my front yard. Essentially my front yard looks like a dust bowl. The yard width is roughly 18m with the eucalyptus tree on the far left and you can see exposed roots all towards the right.

Am I essentially fighting a losing battle trying to get any lawn to grow?

It’s couch grass which has also invaded my garden beds.

Thanks