I would do it this way, but i’m sure a lot of possible ways exist:
Forget the lines, think only about the vertices. You want to create a grid of points, but every second row is ofsetted by the half X distance. So you can forget every second row as well.
Basically you have to find out how you want to distort the the Y distance of a grid. You can use some math for it, or multiple slider inputs, it depends on the use case.
After you built your grid, create the second row of points, than create the lines by two coordinates. I would create the left and right leaning lines separately.
This won’t be an easy ride, you will have to use a lot of list manipulations, try out all the list nodes in the builtin library. But you can create this with the OOTB nodes.
Edit: I was interested how hard is it, it took me 30 minutes to create the graph, here is a demo: https://youtu.be/9WfLOZMD-b8