Any evidence that Linial, Shraibman lower bound on quantum communication complexity is not tight?
I don't know of any function with communication much higher than the $\gamma_2$ bound. However, my intuition of why it is not tight is because the $\gamma_2$-norm is also a lower bound for QCMA communication. See this paper by Klauck for the definition of QCMA communication.

To prove the lower bound on QCMA communication using the $\gamma_2$-norm you can use the same reduction to an XOR game as in the  proof of Theorem 14 of this paper. This will also hold for certain types of entanglement.