Not lend but give - because if it’s a full pay or close to it - that would be an insane amount of borrowing. Agreed on checking the NPC - it could be the student will have many LAC opportunities.
Obviously you have the UCs and CSU.
A U of Arizona will come in near budget as would Alabama - both with auto merit. Many more schools would too. You could do Honors at both and frankly so many publics with merit from a South Carolina to Kansas etc.
Schools such as SMU, W&L and more have full ride competitive scholarships that might interest you.
Let us know what your family need is - as the schools say. That’s not what your parents want to pay but what the schools say they can afford to pay.
An overall 15-20k budget will be tough - and you don’t want to take on debt.
But you’ll have options to get close.
Best of luck.