"nextCount" is a poor choice of name for a constant that is a time delay.
How about "display_delay"?
And "lcdCount" can be "lcd_time" much clearer...
You need to subtract before compare if comparing time values as
they wrap-around, whereas the difference cannot wrap if the delay
is reasonable.
void loop()
{
if (millis() - lcd_time >= display_delay) // subtract before compare
{
lcd_time += display_delay ; // move target a fixed delay
... stuff ....
}
}