Have I achieved a null- terminated C-string through the code?

Are they to be called separately or somewhere else?

What is that loop doing? It is printing one character at a time to the LCD and calling atol() and calling Serial.print() to print count.

What DO you want the loop doing? Isn't it obvious that you want it doing only the first thing? Move the other code outside of the loop.

Since you (will) have count as an unsigned long, and since the LCD can print() an unsigned long, it doesn't make sense to print the digits one at a time to the LCD. So, get rid of the loop, call atol() once, and Serial.print() and LCD.print() count once.