You don't sacrifice lands until Nahiri's Lithoforming is resolving. Once you do so, players can't take actions until the spell has finished resolving.

If X is greater than the number of lands you control, you sacrifice each land you control. The number of cards you draw is less than X, but you're allowed to play X additional lands.

Nahiri's Lithoforming's permission to play lands is cumulative with other effects that allow you to play additional lands, such as that of Scale the Heights.

If an effect says that a land enters tapped unless a condition is met or a cost is paid, that land enters tapped even if that condition is met or that cost is paid if it's affected by Nahiri's Lithoforming.