This appears the be the case:
"A second drawing is held to determine the other lottery winner. Like the first drawing, the second winner can only jump ten spots, but this time it is using the re-seeded order following the first drawing. This second drawing will not affect the team(s) with locked-in positions from the first drawing. If a ten spot jump is to a pick that is already locked-in, this team will receive the next available pick."
So the second lottery winner does not automatically get Pick #2. They get “the pick they are eligible for after a 10-spot jump.” If that slot is already occupied because of Draw #1, they slide to the next open position.
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