What is the impedance of two transmission lines in parallel?
Your schematic would be difficult to realize, because normally the two ends of a transmission line are far enough apart that you can't connect a lumped source across them. The whole point of a transmission line is that it is "long" relative to the wavelength of the signals it carries.

If you connect two transmission lines in parallel (and terminate the far ends with matched loads) like this:







simulate this circuit &ndash; Schematic created using CircuitLab

then you could use the formula you proposed to obtain the equivalent input impedance.