The groups say the president and his handpicked board could bypass preservation rules, while Justice Department lawyers argue the work is limited repairs within board authority.
The dispute follows Trump's overhaul of the centre's leadership and naming, and runs alongside a separate lawsuit by Representative Joyce Beatty over the renovation plans.
Why is a federal judge questioning the cost-benefit analysis of the renovation plan?
How can preservation laws be enforced when a landmark's own board approves the contested changes?
Is a complete shutdown the only way to fix the Kennedy Center's extensive structural damage?
What will happen to the Kennedy Center's priceless art collection during its proposed two-year shutdown?
Can a 'living memorial' survive a two-year closure and a complete change in leadership?