The correct answer is $\boxed{\text{L25P}}$.
The sequence is a simple alternating pattern of letters and numbers, with each letter followed by a number that is 5 greater than the previous number. The first letter is C, and the first number is 4. The second letter is F, and the second number is 9. The third letter is I, and the third number is 16. Therefore, the fourth letter should be L, and the fourth number should be 25.
Option A, K25P, is incorrect because the letter K does not follow the pattern of alternating letters. Option B, L25P, is correct because the letter L follows the pattern of alternating letters and the number 25 is 5 greater than the previous number. Option C, L25O, is incorrect because the letter O does not follow the pattern of alternating letters. Option D, L27P, is incorrect because the number 27 is not 5 greater than the previous number.