Doubt your man served in the CW

Wiley P. Lee fought in the United States Civil War for the Union Side.

Wiley P. Lee
Union Regular Army
16th US Infantry (Regular Army)
http://civil-war-soldiers.mooseroots.com/d/c/Wiley-Lee

The 16th Regiment, US Infantry (Regular Army)was organized by direction of the President May 4, 1861, and confirmed by Act of Congress July 29, 1861. Dept. of the Cumberland, to July, 1865. [1]

OVERVIEW:
Organized by direction of the President May 4, 1861, and confirmed by Act of Congress July 29, 1861. Organized at Chicago, Ill. Ordered to Kentucky October, 1861. Attached to 4th Brigade, Army of the Ohio, to December, 1861. 4th Brigade, 2nd Division, Army of the Ohio, to September, 1862. 4th Brigade, 2nd Division, 1st Corps, Army of the Ohio, to November, 1862. 3rd Brigade, 2nd Division, Right Wing 14th Army Corps, Army of the Cumberland, to December, 1862. 4th Brigade, 1st Division (Centre), 14th Army Corps, to January, 1863. 4th Brigade, 1st Division, 14th Army Corps, to April, 1863. 3rd Brigade, 1st Division, 14th Army Corps, to October, 1863. 2nd Brigade, 1st Division, 14th Army Corps, to October, 1864. Regular Brigade, Chattanooga, Tenn., Dept. of the Cumberland, to November, 1864. 1st Brigade, 1st Separate Division, District of the Etowah, Dept. of the Cumberland, to July, 1865.

SERVICE:
-Camp at Bacon Creek and Green River, Ky., till February, 1862. March to Nashville, Tenn., February 14-25. Occupation of Nashville February 25. March to Duck River March 16-21, and to Savannah, Tenn., March 31-April 6. Battle of Shiloh, Tenn., April 6-7. Advance on and siege of Corinth, Miss., April 29-May 30. Buell's Campaign in North Alabama and Middle Tennessee June to August. March to Louisville, Ky., in pursuit of Bragg August 21-September 26. Pursuit of Bragg to Crab Orchard, Ky., October 1-15. Lawrenceburg-Dog Walk October 8. Perryville October 9. March to Nashville, Tenn., October 17-November 7, and duty there till December 26. Advance on Murfreesboro, Tenn., December 26-30. Battle of Stone's River December 30-31, 1862, and January 1-3, 1863. Duty at Murfreesboro till June. Middle Tennessee (or Tullahoma) Campaign June 23-July 7. Hoover's Gap June 24-26. Beech Grove June 26. Occupation of Middle Tennessee till August 16. Passage of the Cumberland Mountains and Tennessee River and Chickamauga (Ga.) Campaign August 16-September 22. Battle of Chickamauga September 19-21. Rossville Gap September 21. Siege of Chattanooga, Tenn., September 24-November 23. Reopening Tennessee River October 26-29. Battles of Chattanooga November 23-25. Orchard Knob November 23-24. Mission Ridge November 25. Graysville November 26. Pea Vine Valley November 27. Reconnoissance of Dalton, Ga., February 22-27, 1864. Tunnel Hill, Buzzard's Roost Gap and Rocky Faced Ridge February 23-25. Atlanta (Ga.) Campaign May 1-September 8. Rocky Faced Ridge May 8-11. Battle of Resaca May 14-15. Advance on Dallas May 18-25. Operations on line of Pumpkin Vine Creek and battles about Dallas, New Hope Church and Allatoona Hills May 25-June 5. Pickett's Mills May 27. Operations about Marietta and against Kenesaw Mountain June 10-July 2. Pine Hill June 11-14. Lost Mountain June 15-17. Assault on Kenesaw June 27. Ruff's Station, Smyrna Camp Ground, July 4. Chattahoochie River July 5-17. Peach Tree Creek July 19-20. Siege of Atlanta July 22-August 25. Utoy Creek August 5-7. Flank movement on Jonesboro August 25-30. Battle of Jonesboro August 31-September 1. At Atlanta till September 28. Moved to Chattanooga, Tenn., September 28-30, thence to Lookout Mountain and duty there till July, 1865.

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I can only find mention of a Wiley Lee here:

Wiley B. Lee, enlisted in the 16th U. S. Army Infantry, July 4, 1865

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W. W. [sic] Lee, High Hill, Leake County, Miss., June 1, 1863 filed claim for the settlement of effects of his son John Lee, Private, Capt. Boothe’s Company (A), 33rd Mississippi Vols., enlisted March 25, 1862, died at Grenada, Miss. June 18, 1862

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W. J. Lee, Private, Company A, 33rd Mississippi Infantry, enlisted march 15, 1862 in Neshoba County by Captain Booth for 3 years, last recorded present at the Nov/Dec, 1863 muster, no further records

Note, believe he was dropped from the rolls soon thereafter as he does not appear on the next surviving bi-monthly Mar/Apr. 1864 muster roll

Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Mississippi

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1860 United States Federal Census

Name: W P Les
[W P Lee]
Age: 62
Birth Year: abt 1798
Gender: Male
Birth Place: Virginia
Home in 1860: Leake, Mississippi
Post Office: Carthage
Value of real estate: 125/300
Household Members:
Name Age
W P Les 62 Farmer
Elizabeth Les 40
William J Les 21
John Les 18
Martha Les 15
James Les 13
Wesley Les 9
Charles Les 3