Express 0.248 as a fraction in its lowest terms.

To convert a decimal to a fraction, place the digits after the decimal point over a power of 10 corresponding to the number of decimal places. In 0.248, there are three decimal places, so we place 248 over 1000.

$$0.248 = \frac{248}{1000}$$

Both 248 and 1000 are divisible by 2:

$$\frac{248}{1000} = \frac{248 \div 2}{1000 \div 2} = \frac{124}{500}$$

Both 124 and 500 are divisible by 2:

$$\frac{124}{500} = \frac{124 \div 2}{500 \div 2} = \frac{62}{250}$$

Both 62 and 250 are divisible by 2:

$$\frac{62}{250} = \frac{62 \div 2}{250 \div 2} = \frac{31}{125}$$

The number 31 is a prime number, and $125 = 5^3$. Since 31 is not a factor of 125, the fraction $\frac{31}{125}$ is in its lowest terms.

The simplified fraction is $\frac{31}{125}$. This matches option C.

The final answer is $\text{C. } \frac{31}{125}$.