on the image below you should see that I have a large black shape which intersects with some black lines. I need for those black lines to turn white when they intersect with that black shape, but I am relatively new to InDesign so have no clue where to start. Any help would be greatly appreciated.
Select the black stroke shape and copy it, Edit -> Copy.
Select the black filled shape.
Go to Edit -> Paste Into. This will past the stroke object inside the blacked filled shape.
Make sure the black filled shape is above the stroked object. Then turn the pasted in object stroke color to white.
Sample layer view