Adding stripes to a shape

Hi,
I was wondering if there was an easy way to add stripes to a shape. None of the motifs are horizontal lines. I am adding a picture of a letter from Hatch that is similar to what I am wanting. Just running stitch horizontal lines.

EDIT I am adding another example of the horizontal lines I am attempting to learn how to do.

Thanks for any tips!

You can get that look with an open-spaced tatami and travel on edge.