Andi,
You left your lunch hour in Switzerland! The Spanish do not sit down for lunch until close to 2pm. OK, given that the Alhambra, but not necessarily Granada, is a tourist destination, you can eat before that, and long after.
If a restaurant in Spain is closed for lunch by 2pm, well, you haven't missed a thing. It was only designed for tourists. To be avoided. Chicken and chips.