If indeed your disk data is recovered, all the photos are in the same structure. Your LR work is stored in a catalog file that ends in .lrcat. When you reinstall LR, look for and open the most recent .lrcat file. All should be there.
In the future, keep an external drive (or two) with copies of you photo files and your catalog file. It will be less stressful the next time this happens.
By default, the catalog is stored on your primary hard drive. If that is the hard drive that crashed then unless you had catalog backups on a different hard drive all of your work in Lightroom will be lost. But at least you still have your images and can work on them as you find time. I certainly agree with the suggestion to have at least one external hard drive, and allow Lightroom to back up the catalog to that EHD at least on a weekly basis.
Not to step on your toes, but the OP said all the data was recovered. I assume he meant the catalog as well.
The OP indicated that the data was recovered, and that he "assumed" that the Lightroom files were recovered as well. I didn't read anything in the original question to indicate that he definitely had the catalog. Thus, the reason for my answer.