Is it possible for a customer to buy the ingredients-- gyro meat and bread--to take home?

They have carryout available.

Go in and ask

Ask Google or Alexa....im sure there are plenty of authentic recipes out there in the cloud:-)

I don't think they sell, for example, just the gyro meat by itself or just the pitas. But you can certainly order take out and have them leave the pieces deconstructed if you prefer to assemble them yourself when you get home.