Yes, with this box checked No, your partner is still able to claim Lauren as a dependent.
This question is asking of Lauren pays more than half of her living expenses because a child that does cannot be claimed as a dependent. It is extremely rare that a minor supports themselves but that is the way the IRS rules are written.
It is an entirely different question from the screen with did you provide more than half of the support for the household, which applies to determining Head of Household filing status and some tax credits.
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