You are correct it has diverse functions. The QL stabilizes the lower ribs during forced inspiration. The QL is one of the muscles that are referred to as muscles of forced inspiration or accessory muscles of inspiration.
FYI the muscles of forced inspiration are typically used in healthy persons to increase the rate and volume of inspired air.
Any one of the muscles of forced inspiration may be used to compensate for dysfunction in one or more of the primary muscles of inspiration.
A scenario where this is common is within populations that have conditions such as COPD, CRPD, asthma, cystic fibrosis, and individuals who have undergone lung and/or heart transplant. The compensation happens as a consequence of hyperinflation of the lungs. Because their lungs are often filled with excessive air at the end of expiration it becomes difficult to inhale. Hence, it is forced.