Technically, Sessions sabotaged the last case. He could have simply said "We're asking if you're illegal, because:"

• We want to know how many citizens we have.
• We want to know how many illegals are here.
• We want to round-up and deport the illegals.
• etc.

Literally any truthful reason would have been valid, but he went and made up some lie about the Voting Rights Act that didn't even make any sense. Sessions knew the law. He knew the only thing that wouldn't get approved was an obvious lie, and he made an obvious lie.