LWPOLYLINE creating arcs from vertices / edges

You statements and questions are assuming we understand things that are not explained.

Are you writing a DXF exporter, are you using a 3rd party DXF library, or are you calling the native SketchUp export API method ?

You show a screen shot, but it has several curve objects within it. It would be nice if you zoomed in closer and selected the curve you are speaking of in the image.

FTR, SketchUp is a surface modeler, and all curves and circles are represented internally with a series of segmented edges.

Lastly, it would help if you show a snippet of the problem code.
(Please read how to post code in the forum.)