Is there a missing picture log file in LRC

To get a file listing all the missing photos, do the LR menu command Library > Find All Missing Photos. That will make a special collection containing all the missing photos. Then select all those photos and use the Any Filter plugin's Sort command to export a CSV file, which will contain one photo per line. The first column will be the full file path of each photo, and you can add columns containing additional fields as needed.

Other plugins that can export CSV files include Data Explorer, List View, and LR/Transporter.

Develop a Log of Missing Pictures in LRC

I had a computer crash; it is fixed now.  I installed LRC and went through my backups and imported pictures.  Unfortunately, I see many folders with question marks and photos with exclamation marks. Finding them one by one would take weeks.
 
If I get a list of all missing pictures from one catalog, I can tell Windows to find them by file name or some other unique identifier, and save them on my pc.  Then it would be easy to point LRC to one file or folder to find the missing pictures.  I looked online and called LRC Support. I could not find anything online, and the LRC support told me it cannot be done. I have to locate each picture individually (I know that if I see a photo, LRC looks for other photos in the same folder).  I find it hard to believe that a s/w, any s/w won't log the missing info, save the errors, ... such as file name, and other info somewhere in the s/w.  Help please!