I'm having trouble scaling strokes in After Effects
If you created the shape with the rounded rectangle tool, then you won't initially have the same control over the transform as you would if you'd made the shape with the pen tool.  But there's a simple fix.  Just right-click on "Rectangle Path X" and convert to bezier path.  Now you'll be able to use the selection tool to draw a marquis around the individual corner points and animate them however you like (just tick the stopwatch next to "path" to create keyframes).

Just to be clear, don't animate the "Scale" transform property x value.  This will distort the lines, even after they're converted to a bezier curve.  Instead, animate the actual corners of the path.