Having a Wacom (or another type of drawing tablet) isn't exactly a "necessity", but it is highly beneficial, because it allows you more freedom in the expression of your line work. But if one is patient enough, one can do without.
As for parallel lines while using a mouse, I'd suggest using the Ink Pen Tool to assist in the precision, because it has the smoothing option. Here's the idea:
• Increase the Ink Pen tool to the thickness you'd like for the "stem".
• Be sure the Smoothing setting for the pen is set to about 30% or more, to ensure a smooth line.
• On an empty layer, draw a line to represent your stem.
• Then, on the layer panel, right click the layer tab with the stem on it and select "New Stencil From Layer Contents".
• Right click the stencil that was created and select "Guide Mode".
• Either clear the layer with the ink pen stem line, or create a new layer and, with the tool you want to use to make your lines, trace the outline of the stencil, to create your parallel lines.
Here's a video demonstrating the idea:
https://youtu.be/HZPtKgEyc3U
Nothing is easy to the unwilling.