Lectures on Faith (1835) teaches that Adam died after the Fall.
"Lecture Second. Of Faith," Doctrine and Covenants, 1835, 20, 21, The Joseph Smith Papers website, accessed February 10, 2022
37. First Adam was 130 years old when Seth was born. Gen. 5:3. And the days of Adam, after he had begotten Seth, were 800 years; making him 930 years old when he died. Gen. 5:4, 5. Seth was 105 when Enos was born. 5:6. Enos was 90 when Cainan was born. 5:9. Cainan was 70 when Mahalaleel was born. 5:12. Mahalaleel was 65 when Jared was born. 5:15: Jared was 162 when Enoch was born. 5:18. Enoch was 65 when Methusaleh was born. 5:21. Methusaleh was 187 when Lamech was born. 5:25. Lamech was 182 when Noah was born. 5:28.
38. From this account it appears that Lamech, the 9th from Adam, and the father of Noah, was 56 years old when Adam died; Methuseleh, 243; Enoch, 308; Jared 470; Mahalaleel, 535; Cainan, 605; Enos, 695; and Seth, 800.
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41. Agreeably to this account, Adam died in the 930th year of the world, Enoch was translated in the 987th, Seth died in the 1042nd, Enos in the 1140th, Cainan in the 1235th, Mahalaleel in the 1290th, Jared in the 1422nd, Lamech in the 1651st, and Methusaleh in the 1656th, it being the same year in which the flood came.