But what I mean is that its clearly not designed for you to be dropping files onto the local disk.
Video encoding is kind of a corner case in that the size of the data really stops you from doing the whole thing in memory, though the persistance isn't needed in between runs.
Probably what you want to look into is attaching an EBS volume to the job, and doing the work from there.
Lambda is designed to be used for tasks like that, such as resizing images, parsing file etc.