Dear Mr. Lovett,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located Indexes to the Carded Records of Soldiers Who Served in Volunteer Organizations During the Civil War in the Records of the Adjutant General's Office (Record Group 94) that includes a reference card for Lovett, Alexander - 2nd Battalion, Veteran Reserve Corps, Company 14 as well as Lovett, Alexander - Unit: 69th Infantry, Company: E - Enlistment Rank: 1 Lt, Discharge Rank: 1 Lt. Both these index cards have been digitized and can be viewed online through the Catalog.
We also located the Organization Index to Pension Files of Veterans Who Served Between 1861 and 1900, 1949 - 1949 in the Records of the Department of Veterans Affairs (Record Group 15) that includes an index card for 1st Lt. Alexander Lovett, 14 Company, 2nd Battalion, V.R.C. The card indicates that he also served in E Company, 69th Pennsylvania Infantry. See below for an image of that record.
These index cards indicate that there is a compiled military service record and a pension file for Alexander Lovett. We located Letters Received, 1863 - 1917 in Record Group 94 that includes Consolidated Military Officer's File of Alexander Lovett, District of Columbia, 1864, which applies specifically to his time in the VRC. This record has been digitized and can be viewed online through the Catalog. There also may be additional service records for him in the record series Carded Records Showing Military Service of Soldiers Who Fought in Volunteer Organizations During the American Civil War in Record Group 94 that has not been digitized. There should be a pension record for him as well.
To order copies of these records, please fill out a NATF Form 86 for the service records and a and a NATF 86 for the pension records and mail it to Archival Operations Washington D.C., Form 86 – Military, National Archives and Records Administration, 700 Pennsylvania Avenue NW, Washington, DC 20408-0001. You may wish to attach copies of the index cards to your order. You also may place your order online using eservices.archives.gov. For more information see Requesting Copies of Older (pre-WWI) Military Service Records or email the National Archives at Washington, DC - Textual Reference (RDT1) at firstname.lastname@example.org.
We also located in the record series Court-Martial Case File of the Lincoln Assassination Conspirators, 4/15/1865 - 7/3/1865 in the Records of the Office of the Judge Advocate General (Army) (Record Group 153) that includes the item Military Commission Proceedings No. 31: Testimony of Lieutenant Alexander Lovett. These are specially protected records that are not served to researchers. The records have been reproduced as Microfilm Publication M599, which has been digitized and can be viewed on Fold3. There is also a transcript online. Finally, in addition to the Court-Martial Case Files, the National Archives has at least 6 additional record series related to the Lincoln assassination. For copies of these records, please contact RDT1 via email. The RDT1 staff may be able to suggest additional record series.
In regard to photographs, the National Archives at College Park - Still Picture (RDSS) has a limited number of photographs of American Civil War era military subjects in their holdings. Please contact RDSS via email at email@example.com to request a search. However, please note that it was not standard practice for the Army during the American Civil War to photograph all soldiers or all units. Photographs of individual soldiers almost never show up in personnel or pension files.
We hope this information is helpful. Best of luck with your family research!