Did I understand you correctly in saying the sinner provides and slays the Lamb? Therefore when John saw Jesus, he reconized Him as the Sacrafice God provided for the sins of the world. John knew the qualifications for the sin sacrafice and it was revealed to him that Jesus was the one and only Lamb without blemish. The scriptures tells us we are all like sheep and we have all sined, except Jesus.
The sins of the world encompasses Jews and Gentiles. Not just one particular sin but ALL sins of EVERYONE. Even so as Gentiles we have not practiced the sacrifical laws of Moses we are covered by the Blood of Jesus.