Between the Confederate offensives into Maryland and Pennsylvania, and the battles which took place in the Midwestern border states, I can imagine that Union forces may have requisitioned food, supplies, horses, and shelter from civilians without their enthusiastic consent.
Did any people sue the Federal government after the war for violation of the Third Amendment?
The text of the Third Amendment states:
"No Soldier shall, in time of peace be quartered in any house, without the consent of the Owner, nor in time of war, but in a manner to be prescribed by law."
Billeting of soldiers in private houses is therefore specifically only prohibited in times of peace. It is permitted in times of war as long as it is done "in a manner prescribed by law".
I'll leave commenting on whether any lawsuits were brought due to unlawful quartering of soldiers to someone more qualified than myself.