Jesus on the cross
Was Jesus naked on the cross because the Roman soldiers cast lots for the undergarment as described in John 19:23-24? Also, it is unusual that there is a distinction between clothes and undergarment. However I do not know how to translate the original Greek that may have some insight on this section.
Your first question is one that remains unanswered. History tells us that it was common practice for crucifixion victims to be naked. That was part of the shame and humiliation of the public execution. The Bible does not specifically mention the nakedness of the crucifixion victims on Calvary, but if that is what Jesus endured, it is another example of how he “humbled himself by becoming obedient to death—even death on a cross! (Philippians 2:8)
The Bible does tell us that the four soldiers assigned to oversee Jesus’ crucifixion divided his clothing into four equal parts and cast lots for his “undergarment” (some Bible translations: “tunic”). The original Greek simply has different terms for clothing in that verse.
Those seemingly insignificant details about Jesus’ clothing point to fulfillment of Old Testament prophecy: “They divided my clothes among them and cast lots for my garment” (Psalm 22:18). Jesus is the Christ, the anointed one, the Messiah.