You asked "How should I go about troubleshooting?"

I would do something like the following:

1. Copy all images from SD card to another location (so you are working with copies and don't risk damanging your originals).
2. View images in new location using Windows File Explorer, or Mac equivalent. If the Operating System is showing the lines, then the photos are likely already corrupt before touching Lightroom.
3. Export one of the corrupt photos from Lightroom to jpeg and check whether the jpeg shows the corruptions in File Explorer or equivalent - this is testing whether the issue is just with Lightroom rendering the image within the application.
4. Import the images to a different computer. This is testing whether the first computer's video display functionality has a fault (such as corrupted drivers or hardware fault). If the stripes still appear, then the issue is not likely due to video card or drivers.
5. Take new photos onto same SD card without formatting the card. If new images don't have the issue then it's unlikely lightroom - more likely a corruption to your old data.
6. If new images do have corruption then use the same camera with different SD card and import again. If these images do not have stripes, then it's likely the SD card. If they do, then it's not your old SD card.
7. If those images did have corruption, then you could test your import cable or SD card reader by swapping it out with another one, but I would expect it quite unlikely to be the source of the problem, and at this stage would suspect the Lightroom software to have an issue. Search for updates to your Lightroom software and install them, then try again.

Failing the above I would have to think it through in a bit more detail.