Lessin, along with his regiment, were surrendered to MGen. Grant's forces July 4, 1863. They were while still organized as a unit, paroled on July 8. Within a few days, they most likely marched out headed as a military unit, for Enterprise, Mississippi where they remained in parole camp until they were exchanged, and then went back on Confederate duty.
Where the information that he deserted on the date, July 15 is a mystery, it is not in his records.
You will note in the website developed by the late Art Bergeron, see below, that he was not alone in "deserting" for West Louisiana. I would guess these troops, many conscripted/drafted men, were fed up with the war, and headed for home waters instead of staying to fight again.
What is interesting in this website, is that he apparently became a member of the UCV, United Confederate Veterans. Similar to the Federal Grand Army of the Republic, GAR. Membership in the UCV would indicate he was held in good standing with his fellow Confederate comrades.
I have been unable to locate a history of the regiment.
I list the information found on the cards found in his file. Note also, there was correspondence with the US Army and Louisiana Board of Pension Commissioners, ca 1925. This would indicate that either he, or his widow filed for a Confederate pension. You should be able to obtain these applications papers through the service noted in the Red enclosed box above. These papers may shed some light on his post Vicksburg adventures. [See below, it appears that it only consists of War Department papers]
The 1920 Federal census has a L. Abshire, age 78, living in Vermillion, Louisiana. I can delve no further into Ancestry.com
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Lessin Absheir
Residence was not listed;
Enlisted on 10/20/1862 as a Private.
On 10/20/1862 he mustered into "D" Co. LA 1st Heavy Artillery
He deserted on 7/15/1863 at Vicksburg, MS
(Estimated date of desertion. Went to West LA)
He was listed as:
* On rolls 4/1/1863 (place not stated)
Sources used by Historical Data Systems, Inc.:
- Index to Compiled Confederate Military Service Records
- Record of Louisiana Confederate Soldiers
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
National Archives Compiled Service Record cards:
Lessin Absheir, Private, Company D, 1st Louisiana Heavy Artillery
Card #
2 - Correspondence with the Adjutant General, War Department and the Louisiana
Board of Pensions, dated Dec. 22, 1925
Enlisted Oct. 20, 1862 as a Conscript at Vicksburg
Captured at Vicksburg July 4, paroled July 8, 1863
Recorded on the Dec. 31, 1863 as "Absent, paroled, absent without leave since
fall of Vicksburg, Went to Louisiana"
Recorded on the Feb. 29, 1864 as "Deserted at Vicksburg after the fall of the city
and went to West La."
3 - Muster roll for Oct. 31, 1862, recorded as Present, Conscript, assigned at Vicksburg
Oct. 20 & joined Co. D
4 - Nov. & Dec,, 1862 muster roll, Present
5 - Jan. & Feb., 1863 muster roll, Present
6 - Mar. & Apr., 1863 muster roll, Present
7 - June 30 to Oct. 31, 1863, [at Enterprise, Miss. on 10/31] Absent, Paroled, Absent without leave since fall
of Vicksburg, Went to La.
8 - Nov. & Dec., 1863 muster roll, Absent, Paroled, absent without leave since fall of VBurg,
Went to La.
9 - Jan. & Feb., 1864 muster roll, Deserted at Vicksburg after the fall of Vicksburg, Went to
West Louisiana
10 - Captured at Vicksburg July 4,1863
11 - Opposite side of parole certificate
12 - Parole certificate at Vicksburg dated July 8, 1864, no further records
3rd Sergeant Trasimon Soileau's record shows the same path
Note: There were four subsequent muster rolls in the records for Co. D through the period March/April, 1864. As he was no longer recorded, this would indicate he did not return to the command prior to May 1, 1864
Also, the Record of Events for the muster roll for the period March/April, 1863 shows they were stationed May 1 " . . at Lower Garrison [South Fort], Vicksburg," noting "The men were all conscripted in western Louisiana sometime in August in 1862. No descriptive lists were sent with them. Attached to this regiment October 20, 1862."
M320: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Louisiana
*******************************************
1st Regiment, Louisiana Heavy Artillery (Regulars)
1st Regular Artillery Regiment was organized during the spring of 1861 with men from New Orleans and the surrounding area. The unit contained ten companies, but there were a number of consolidations during the war, and in 1865 it appears that only four remained. A heavy artillery unit, it served at Forts Jackson and St. Phillip at New Orleans, then was part of the river batteries at Vicksburg. Here it was captured on July 4, 1863. After being exchanged and reorganized, it was stationed at Mobile and saw action at Fort Gaines, Fort Morgan, and Spanish Fort. On May 4, 1865, the unit surrendered with the Department of Alabama, Mississippi, and East Louisiana. The field officers were Colonels Johnson K. Duncan, C.A. Fuller, and Paul O. Hebert; Lieutenant Colonel Daniel Beltzhoover; and Majors James B. Anderson, W.C. Capers, Henry A. Clinch, and Raymond Montaigne.
NPS Soldiers and Sailors System
....................
xABSHIRE, Lessin. Pvt. Enlisted in Company D, 20 Oct 62, no place given. Probably a conscript. Present to Apr 63. Absent 30 Jun-Dec 63, paroled, AWOL since fall of Vicksburg, went to LA. Jan-Feb 64, "Deserted at Vicksburg--after the fall of the city--Went to West La." No further record in Booth. Buried Holy Rosary Catholic Cemetery, Kaplan; his UCV grave marker calls him Lessin ABSHIRE. // Booth, LA Confed. Soldiers, 1:23: Lessin Absheir. CSRC, Index: Lessin Abshier. // [photo]
http://www.acadiansingray.com/1st%20Regt.%20Hvy.%20Arty.htm#Company%20D
See also: http://www.civilwaralbum.com/vicksburg/higgins_report.htm
Louisiana State Archives: Confederate Pension Applications Index
http://www400.sos.louisiana.gov/archives/gen/cpa-alpha.htm
Louisiana Secretary of State
Confederate Pension Applications Index Database
Selected Name Detailed Data
Reel: CP1.1 -- Microdex 1 -- Sequence 10
Target card: ABSHIRE, LESSIN
Applicant Information & Name Variations:
ABSHIRE, LESSIN
Parish: VERMILION -- Pages: 26
Soldier Information & Variations:
ABSHIRE, LESSIN
State: LA
Branch: ARTILLERY
Unit: 1ST REGIMENT HEAVY
Company: CO. D
(Above military data is from the War Department.)