I'm sute a feature could be added to Photoshop. However it would be a complex feature,the Master file would need meta-data added to record information like the last number added, number of output watermarked image file permitted, where to store the watermarked files and other options also need to be recorded in the images metadata like font, font style, Font size relative to image size position information etc.
This is not a current feature in Photoshop so now you would need to use Photoshop scripting to do it in Photoshop. I do not use Lightroom for it does not support layers so I do not know if Lightroom can be scripted. I know you can not add text layers for layers are not supported in Lightroom. Information may not need to be recorde if all the output file will be created in a single process. Still the information is need for the run and it will take some time to watermark and save 1500 image files it would of course take much longer to print 1500 images..
Though the concept is basic the process would be complex and long running.
This is from 2011 Lightroom.
It seems to work, but I didn't find a suitable saving method without a diashow frame.
As I can't script, I would use variables/data driven graphics.
Yes a Template PSD file with a Text Variable layer and a 1501 line CSV file could create the Print Image files. Still it will take some time to watermark 1500 Document and save them for printing.
Duplicating the File1500 time with sequential filenames 1-1500, 2-1500, ... 1500-1500. The using my Batch Collage populating to stan the file name on the collage could also be used. Or batch a simple script to stamp filename on the images
If you are printing this yourself at home and you only have a printer driver, do you really wish to have 1500 hi-res images waiting to be printed when/if you get an order? If these are not print on demand and you will stock them, do you really wish to have 1500 printed images physically stored?
If you are having these printed by a print service provider, they will likely have a RIP that will eat it's way through the 1500 images... However they probably don't wish to RIP essentially the same image 1500 times.
This is what a dedicated variable data processing RIP is for, the static image would be sent and RIPed once, then the variable content would be automatically added 1500 times – greatly increasing productivity.
If I was going to print these myself on demand I would probably just have a single image with editable text and manually increment the number each time a limited edition print was sold.
If I was going to print these myself and wanted to pre-populate all of the serial numbers, then I would likely do this in a PDF, where each page could reference the same single image and only the text would be variable.
So as well as the technical/mechanical aspect, there are also logistical and practical aspects to consider too.