I am not sure what criteria you have in mind for creating the lines, but once you have the lines that you want to use to split the polygons, you can try the following: 1. Run the Intersect tool to find the line segments that are intersecting/inside the polygons. 2. Run Feature To Polygon tool (requiring ArcInfo license) using the output lines from step 1 and the polygons as input. The result should be the split polygons.
I have shapfile also with around a thousand polygons. Each polygon will need to be split based upon its area, if a polygon is greater than say 3500 sq.ft. then it will need to be split, but if not greater then it doesn't. Is there a way that this can be accomplished?