This would also imply that simply experiencing a homosexual attraction is a deadly sin.
Gen 19:4 But before they lay down, the men of the city, [even] the men of Sodom, compassed the house round, both old and young, all the people from every quarter:
Gen 19:5 And they called unto Lot, and said unto him, Where [are] the men which came in to thee this night? bring them out unto us, that we may know them.
Were the men "homosexually attracted"? Yes. Was it a "deadly sin"? Yes.
I dont know of any Christian tradition that teaches this.
I'd suggest reading the Bible instead of Vatican Position Papers.