I presume you mean this Dr. LLoyd? https://www.findagrave.com/memorial/34005700
If you have an account on Ancestry, you should search the user generated family trees. I found the following listings for him. Clicking on these these results bring up some rather detailed research that others have already done about him, which may save you a lot of time reinventing the wheel as well as suggest ideas for further research. As you can see, the first three are the most complete. For the most part they agree on the facts, though I did find some minor disagreements between the three as well as some details in one but not the others.
The Lloyd Family tree, for example, gives the following listings for his parents and siblings.
Thomas Newton Lloyd
Jasper L. Lloyd
Samuel W Lloyd
Thomas Newton Lloyd
Martha Ann Lloyd
James Emory Lloyd
Susan Jane Lloyd
William Milton Lloyd
Joseph Jackson Lloyd
Pvt. Benjamin Franklin Lloyd
In regards to deaths of siblings during the American Civil War, the Lloyd Family tree gives the following.
Death of Brother Pvt. Benjamin Franklin Lloyd (1842–1862)
11 Sep 1862 • Warrenton, Fauquier, Virginia, United States
Death of Brother William Milton Lloyd (1839–1863)
27 Jun 1863 • Vicksburg, Warren, Mississippi, United States
The Vincent 2017 tree adds the detail that Joseph Jackson Lloyd (twin to William Milton Lloyd) died in 1865.
Dear Mr. Lloyd,
Thank you for posting your request on History Hub!
If they served in the Confederate military forces, there may be a record of them. We searched the National Archives Catalog and located Carded Records Showing Military Service of Soldiers Who Fought in Confederate Organizations in Record Group 109 which includes records about individual Confederate soldiers based on information abstracted from Union prison and parole records and from captured and other surviving Confederate records. This series is indexed by General Index to Compiled Service Records of Confederate Soldiers. Portions of both series have been digitized and can be viewed online through the Catalog by clicking on the blue “Search within this series” button. We searched the series and located Confederate Soldiers from the State of Georgia - Lloyd, G W - Floyd Legion (State Guards) that might be a match for George Washington LLoyd. However, it does not provide the names of any family members.
The type of Civil War records most likely to have information about family are pension files, and no pensions were provided by the federal government to former Confederates. Also, because of the circumstance of the war, not all Confederate military records survived and were acquired by the federal government, so there may be persons that served that are not included in this series.
To order copies of records from this series not yet digitized, please fill out a NATF Form 86 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.
Please note that the National Archives and Records Administration has suspended reproduction and digitization services until further notice due to COVID-19. Orders will not be serviced until operations can resume safely. We apologize for any inconvenience. Once operations resume, document reproduction requests will be filled in the order in which they were received.
You can also search the Civil War Soldiers and Sailors System (CWSS).
Please note that both the Carded Service records and the CWSS often omit middle names, and sometimes use initials or abbreviations (such as “Wm” for “William”) instead of full names.
We hope this information is helpful. Best of luck with your research!