Dear Mr. Slack,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located a series titled Records of the 1st Through 338th and the 559th Infantry Regiment, 1916-1921 in the Records of U.S. Regular Army Mobile Units (Record Group 391) that includes records of the 156th Infantry Regiment. We also located Records of Divisions, 1917 - 1920 in the Records of the American Expeditionary Forces (World War I) (Record Group 120) that includes the 39th Division and may include records of the 156th Infantry Regiment which was a part of that division. Plus, we located Records of Infantry Brigade, 1917 - 1919 in Record Group 120 that should include records of the 78th Infantry Brigade to which the 156th was assigned. For more information about these records, please contact the National Archives at College Park - Textual Reference (RDT2) via email at firstname.lastname@example.org.
Due to the COVID-19 pandemic and pursuant to guidance received from the Office of Management and Budget (OMB), NARA has adjusted its normal operations to balance the need of completing its mission-critical work while also adhering to the recommended social distancing for the safety of NARA staff. As a result of this re-prioritization of activities, you may experience a delay in receiving an initial acknowledgement as well as a substantive response to your reference request from RDT2. We apologize for this inconvenience and appreciate your understanding and patience.
Because the 156th Infantry Regiment was initially part of the Louisiana National Guard, the Louisiana State Archives may have additional records concerning the unit. Lastly, you may wish to contact the Louisiana National Guard Museums, the State Library of Louisiana, and the National World War I Museum.
We hope this is helpful. Best of luck with your research
In case this helps, FamilySearch.org has a collection called United States, World War I, Military Muster Rolls and Rosters, 1916-1939. It has the rolls for the 156th infantry from roughly Aug. 1917 onward (some companies vary slightly on the start date). There is a notice at the beginning that says, "For prior rolls see 1st Louisiana Regt N G".
The records are grouped by Organization (156th Inf), then Company name, then from the oldest to newest. You have to go page by page. There is a page in between each company that says "New Orgn Begins".
This link takes you to the first page of 156th Infantry (it's image 541 of 1962 total)
(This link takes you to the overall search page where you can search for different units--just use the Find button to search by the number.)
You will have to register (for free) to view these.