Making independent animations

As title suggests, I want to make the objects on the screen move idependently one from another. I want to make a game like Space Invaders for example, and I have encountered some problems. One of them would be that I can’t make the bullet move without erasing all the content from the screen. I found a solution that works, by redrawing the ship everytime, as longs as the bullet travels, but in the meantime, I can’t move the ship up or down.

    for(int i=1; i<=16; i++)
      {
        lcd.setCursor(0,1);
        lcd.write(byte(0));
        lcd.setCursor(i,1);
        lcd.write(1);
        delay(150);
        lcd.clear();
      }
      lcd.setCursor(0,1);
      lcd.write(byte(0));