2001 Lincoln Cent Possible Double Die Obverse

You looking way too close. The outlines are probably cause by die polishing that entered in that the face area. When the reduction of the fields happen, it will show as a raised area on the coins struck by that die. That is not what a doubled die is. This is just a die event that happened to the die that struck you coin. A doubled die has the doubling on the die from coin #1 struck by it. Also an issue with the hub process on these single squeeze dies alters the central devices more than others. The 2001-2003 devices on the cents those years had an appearance of wider devices. But because they all look like that none are considered a die variety as all are that way.
2001P-1DO-001 DDO:




So here are some side by sides as to what to look for on these:



Note the centers of the devices appear wider. The centers of the closed devices are smaller. Always look at the center area of the devices and not concentrate on the outside edges, as that is where Machine Doubling is found. Hope this helps.

There is only one example of nose doubling and that is on the biggest DDO:

But I'm not seeing any doubling on your coin. (My example was a Plain mintmark) But the spread will be seen on the centers of the devices.

The 1999-D DDO cents look like this SBS a normal image and Jim's coin which is a match to that die number:




Knowing where to look helps ID a matching doubled die.