You could always add Filename-Sequence while importing and renaming your images.
To refer your images easily you need to manage them using collections,smart collections etc.
My library is very organized into collections, etc. I want a continuous numbering system for clients to interact with when file choosing. A Filename-Sequence doesn't really work for the way I have my images for the multiple repeat clients. Any other suggestions? My desire is for each and every file to have a unique number.
You could also consider renaming the exiting images in Lightroom:-Press F2 rename them with Filename(custom) -sequence(Each file will have own sequence number.)
Remember the last sequence number and import new files with same custom name and next sequence number.
I seem to remember that Bridge or perhaps Photoshop, years ago, allowed you to automatically have the number sequence added when you wanted to add new photos to a given file name. So if I knew I had photos named "Great Wall" but didn't remember what the last number in the sequence was, and now 2 years later I want to rename some new photos with the "Great Wall" name, the program would automatically ask if I wanted to continue the sequence. You say that it is necessary to remember the last sequence number. Isn't there still some way to have it done automatically? It seems like a step backward to have to remember the sequence number. I am writing about doing this in Lightroom CC