Responsive background images in carousel
It's not really a Craft CMS question, but...

I don't remember Flickity supporting what you describe. You could try listening for screen size on pageload (and resize), assigning the correct image to the cell, and then creating the slideshow (destroying it first if it's a resize).

But half the point of lazy loading is to avoid loading images until they're needed anyway, so I'd question whether serving different images for different sizes is the right approach. Probably the easiest method would be to forget lazy loading and use an inline &lt;style&gt; element with media queries targeting each cell.