The best time to sow any grass seed is late summer. This is because the heat has built up in the ground, and it has moisture at this time of year. There is also less weed growth in late summer, so less competition for the seed.
The next best time would be mid-spring, though you may have to water the lawn a lot if it is a drier than average season.
Also, bear in mind that there is the option of a roll-out lawn, which is available all year round at a competitive price.
I hope this answers your query, and please feel free to reach out if you need any further help.