You can plot the data at numerical locations (1,2,3,4, …). Then, use the Axis settings to change specify the labels at each location.
Here is a link to show how to change the tick mark labels to text:
Axis settings > Labels
In terms of creating the lines themselves, the best way would depend on how your data is set up. If you have this many lines, I would recommend having the data flattened, where there is some categorical column that you use to determine the color.
How to flatten data