How does Vorinclex's second ability work at the time of his death?
They will not untap as usual in the next untap step.

The reason is that after the ability triggered (while Vorinclex was alive) it went on the stack as a replacement effect for the next untap step.

When Vorinclex died, it didn't undo that effect.

Any lands tapped after Vorinclex died would untap in the next untap step.

If Vorinclex instead said something like "While Vorinclex is in play lands do not untap as usual" then it's death would change the situation.