The lien imposed by § 47-4421 shall be deemed to have arisen at the time the assessment is made, or if the tax return is not timely filed, on the due date of the tax return, and shall continue until the liability for the amount assessed (or a judgment against the taxpayer arising out of the liability) is satisfied or becomes unenforceable; provided, that:
(1) A lien for the tax imposed by Chapter 20 of this title or § 47-1812.08 shall arise on the due date of the tax return; and
(2) A lien for the taxes imposed by Chapter 37 of this title shall arise on the date of death.