You probably have a picture of a professional baseball field in your mind when you're comparing your patterning vs. what you're trying to get.
The "lines" you may be hoping for occur because the turf is literally rolled flat in different directions. The significantly smaller footprint your mower leaves in an attempt to create the same effect is incomparable.
Perspective is everything: The elevated vantage point you captured these pictures shows a pretty harsh view of the lawn and many of its imperfections. Also consider the size of the lawn, vs. the size of the mower's footprint to reemphasize the point above; Take the upper right hand quarter of the lawn in the picture. If the entire front yard was only that large, the effect would appear a lot closer to what I imagine you had in mind.
For what it's worth to you, the obvious, deliberate variation in your mow lines coupled with the fact you'd post this question on a forum in the first place are a testament to your professionalism. That customer is lucky to have you.