Whether a collapsed lung will heal on it's own without medical treatment will depend on how bad the collapsed lung is and what caused it.
Most times when the lung isn't collapsed too bad then it can heal on it's own but still you should always seek medical treatment so you know exactly what treatment is needed for the collapsed lung.
If the collapsed lung is more serious then you may need surgery to fix the collapsed lung otherwise the collapsed lung could become fatal.
Sometimes though if the collapsed lung isn't all that serious then a surgeon can use a needle and syringe to remove the air and fixed the collapsed lung.