if many people started posting pictures, wouldn't that overload Lemmy completely?

Depends on the instance, some are well-prepared and can expand storage depending on the traffic, so I think they'll be fine. People are already posting a lot of images, but it is a good idea to try and link to other sources rather than stress the servers.

In the future we'll have flying cars and images will be stored long-term as Dall-E prompts, and will be generated on demand. Future archeologists will never know why people posted so many pictures of cats with weird limbs