Who was the young lawyer? Abraham Lincoln.
What was the unique distinction the patent acquired? Lincoln is the only president to date to hold a patent.
Abraham Lincoln was the young lawyer Patent #6469 for a device to lift boats over shoals; It gave Lincoln the distinction as the only US president to hold a patent.
Edit - I considered marking a lot of answers wrong, since the question did not ask what distinction the young lawyer eventually acquired (which was that it made him the only U. S. president to hold a patent). It asked what distinction the patent acquired (which was being the only patent held by anyone who ever became U. S. president).
However, since the official answer is that it made him the only president to hold a patent, I have to give credit for that response. Of course, those who gave the answer that it was the only patent held by anyone who became president will also get credit.