$\omega$-regular expression to LTL
LTL is less expressive than $\omega$-regular expressions. For example, the expression 
$$((a+b)b)^\omega$$
i.e. "there is $b$ in all the even places" 
cannot be expressed in LTL.

In addition, observe that checking whether an $\omega$ regular expression is expressible in LTL is harder than checking universality, which is PSPACE hard.

However, there are ways to tackle this problem. You can start here for a reference.