I wanted to know if there are any standards on how we can visualize different attributes by mapping them with different shapes so that they are distinguishable in parallel coordinates?
I am not sure exactly what your questions is asking.
Are you asking about adding markers to the points where the lines of a parallel coordinates plot intersect the axes, with shapes that indicate some property of the line?
If so, I’m not sure that parallel coordinates are a special case compared to other kinds of visualisations that use different marker shapes, such as line-graphs or (multi-class) scatterplots.