These look like pressed hair grooves in the 2001 penny but I am no expert and have never found anything like this. Is this a pressed hair or lent error coin? I just found it today in circulation. It looks to me like one big long hair or maybe 2. It is definately grooved into the coin, not superficial. Well, I know I'm not supposed to do this, but I cleaned the coin with a little brasso and the lines are still there. They are not as dark, but they did not come off with some of the other dirt... Looks like a Strike Through Abnormal Objects(hair) so it would be a strike error.
It is very hard to tell from your photo. Look at the marks under high magnification. If they are a strike thru then you will see the lines are indented into the field. I see smudges that look like oil was on the surface of this coin and the oil left discolored blotches. If the fibers came in contact with the coin at the same time then maybe what you are seeing is the same discoloration but in the shape of the fibers from the oil on them. If this is the case then it is just post mint damage. So check to see if the lines are just a discoloration on the surface or if they are indented into the surface.