Buy Lawn seed really helped along by Mycorrhiza
The seeds are a mixture of two Perennial Ryegrasses ( Lolium perenne) 'Barbarado' and 'Fandango' both are especially tolerant of drought conditions, tolerant of low temperature germination, but very heat tolerant.
These are backed up with Red Fescue ( Festuca rubra rubra ) which really stands up to wear and tear ( aka "families" !) Enough for about 35 square metres if you are heavily 'patching', or 25 square metres for sowing over a lawn.
Mycorrhiza, nature's age old natural growth aid, will really make the grass grow under your feet !