Seems like your original images are not stored on dropbox.
Where are your original images stored?
If they are stored locally on your machine, you might have to relocate the images.
Also, it is not suggested to store the Lightroom Catalog on a network location.
If you want to use the same catalog on two different machines, you can store catalog on an external drive and the original images on dropbox.
That's right, the original files are stored on an external hard drive. But the catalog is finding the original files OK. It's just the thumbnails that it can't find.
Are you saying it's not a good idea to store a catalog on dropbox? The problem with storing a catalog on an external drive is that I have to keep moving the drive between the computers. Also storing original images on dropbox would use up a lot of space.
Thanks for taking a look at this issue in any case.
Can you show us a screenshot?
If the images are missing, you should relocate the images. Refer this article for steps : How to find missing photos in Photoshop Lightroom
It is not suggested to store the catalog on dropbox as that might show some unexpected behaviours as we have observed. You can refer this article : Lightroom catalog FAQ
You can store your original images on external drive as well.