Small animated display with LCD and SD card?

Can it be done? Something like animated GIF from SD card (where individual images are stored) and then displayed on a small LCD? I'd love to have something that from a distance looks like a padd from Star Trek: Personal Access Display Device | Memory Alpha | Fandom (first image)

They would be non interactive (no touch screen, no button, etc) and the LEDs on the bottom can be plain vanilla flashing LEDs.

Is Arduino fast enough to fetch data from SD card, display it on (I think) 2.8"-ish display (the closest size I can find to existing color LCD shield), and change image every few seconds?

"Every few seconds" should be no problem.

This $40 2.8" device from adafruit includes a touch screen:

Hmmm better than I thought. Since the touch feature will be built in anyway maybe I'd just make the project use a speaker and if anyone touches the display it'll let loose a blood curling scream.