Here are some questions to help troubleshoot this:
- have you confirmed you are updated to the latest versions of iOS and Lightroom? If not, please update both and try again.
- was the SD card formatted by a camera? Specifcally, do all the photos reside inside a DCIM folder?
- can the iOS Photos app see the same photos? I know you said the Files app can access the card's contents, but similar to the bullet point just above, I wonder if the card and its contents are organized in a way that's compatible. Anything that's visible to iOS Photos app should also be visible to Lightroom.
- if none of the thoughts above help, can you share what camera model you are using?