Rotating cylindrical shell source for Lewis spacetime

Rotating thin-shell-like sources for the stationary cylindrically symmetric vacuum solutions (Lewis) are constructed and studied. It is found, by imposing the non existence of timelike curves in the exterior of the shell, and that the source satisfies the weak, dominant and strong energy conditions that the parameters, commonly denoted by $a$ and $\sigma$, are restricted to $0 \le \sigma \le 1/4$ when $a > 0$, or $1/4 \le \sigma \le 1/2$ when $a < 0$.