At 12:45 he’ll have lunch

This says that at 12:45, the subject will stop what he was doing and start to have his lunch.

At 12:45 he’ll be having lunch

This says that at 12:45 the subject will be engaged in having lunch, he may have just started, he may be nearly done, we don’t know.

Is it true that if he goes to lunch next Thursday, he’ll eat a carrot and make steamed rice at 12:45?