Can you apply granules fungicide and fertilizer to a lawn at the same ?
You could. However, there are several reasons why this is not suggested.
1) First and foremost and before you proceed with either fungicide or fertilizer, make sure the SOIL PH is okay. When your PH gets out of balance, things tend to go wrong with the grass and other plants. Since you're wanting to apply a fungicide, it sounds like you may already have a problem. And if you do, start with making sure the PH is in check.
2) Since fertilizer can "feed" a fungus, it's always best to do the fungicide treatment first, before any fertilizer, to make sure you don't enhance the fungus. Now if you're only applying a fungicide as a preventive treatment, don't worry; both can be done at the same time. But if you have active fungus growing, treat for it first waiting at least a few days to let the granules get activated and then you can proceed to using the fertilizer.
So in summary, if you treat with granular fungicide and water it in within a day, you can apply some fertilizer as early as 3 days later and not worry about "helping" any existing fungus already established. Here are direct links to the information mentioned above:
Soil PH Control: http://www.soil-ph.com/soil-ph
Lawn Fungus Article: http://www.bugspray.com/article/fungus.html