Blue lips and tongue are a sign of central cyanosis. This means that for some reason the level of oxygen in the blood is less than it should be. The most common cause of this is cyanotic congenital heart disease (this sign would be present at birth or soon after birth).
There are many other causes of central cyanosis, but one of the most common is a severe respiratory problem such as infection. Oxygen consumption is increased when a child has a fever, and thus central cyanosis is more likely.