Member objects are declared like other variables
private:
LiquidCrystal lcd;
The initialization of those objects happens at constructor time, with a syntax that looks like this:
Arduino_Marquee::Arduino_Marquee(int RS, int ENABLE, int D4, int D5, int D6, int D7, int LCD_COLLUMN, int LCD_ROW)
: lcd(RS, ENABLE, D4, D5, D6, D7) {
... more code ...
}
It's ok instead to save the rows and columns values and use them later when calling lcd.begin(). The reason is begin() is a "normal" method of the LiquidCrystal class, not its constructor.
Also a note about coding style: capital letters are usually used for constants and #defined symbols...
Anyway, I'd initialize the lcd object in the main sketch and just pass a pointer to it to the Marquee class, but that's just how I'd do it... 