What come to my mind first is checking the geometry. If the files comes form a different app then there is a change you have some unlucky geometry situation here. Overlapping objects or surfaces sitting perfectly on each other etc. A second thing to check can be when you turn off adaptive in the dome light. Had some sprinkles there in specular a few days ago in an outdoor scene. Turning it off solved it. So hoping one of those things helps!
With animation you would need to lower the noise threshold to at least 0.01 and raise min/max subdivs. What works depends on your scene, but I would say min 3-4, max 16-24 and noise threshold 0.01 or 0.008 would work. The flickering you are seeing is happening in the blackest parts of the image (in grass) which means only min of 1 subdivs is being reached there. For the LC same thing, retrace of 8 is enough for animation but what I would do is use camera path and calculate LC first to a file, then load the lc saved file and render animation, this way you will not have to calculate LC per frame and it will produce a more stable result.