One of the functions used in ITUbee's round function is $L$ which is defined as $L(A, B, C, D, E) = [E \oplus A \oplus B, A \oplus B \oplus C, B \oplus C \oplus D, C \oplus D \oplus E, D \oplus E \oplus A]$. Is this operation invertible?
Yes, it's invertible. Consider:
$(E \oplus A \oplus B) \oplus (B \oplus C \oplus D) \oplus (C \oplus D \oplus E)$
to get the value of $A$. The values of $B, C, D$ and $E$ can be calculated in a similar manner.