Without actually seeing your property I will guess you have a mix of Zoysa grass and an old cultivar of Fescue.
The best fix would be to erase the lawn using Roundup and get rid of both varieties and reseed with the new variety of what they refer to as "dwarf tall fescue". This is a rhizobial grass that travels from the root system these new varieties are heat tolerant and have better color performance and if you plant at the high seed rate you should get a good looking lawn. Keep in mind that Roundup will have no effect on the dormant zoysa the temperature should be in the mid 70s or 80s to get a good kill on the zoysa. The fescue should succumb to a Round up application.
I hope this is helpful
Best Nancy and Happy Yardening