Identify the word that cannot be formed using the letters of the word “ENLIGHTENING”, without repeating any letter more times than it appears in the original word.

Let's count the letter frequencies in “ENLIGHTENING”:
$\text{E:2, N:3, L:1, I:2, G:2, H:1, T:1}$.
Now examine the word "TENNIS": it contains the letter 'S'. The letter 'S' is completely absent in “ENLIGHTENING”. Thus, "TENNIS" cannot be formed.