How can a situation occur where a lower-priority queue gains access to resources before a higher-priority queue?

This can happen due to priority inversion.

Priority inversion occurs when a low-priority task holds a resource (e.g., a mutex) needed by a high-priority task. The high-priority task is blocked, waiting for the resource to be released. Meanwhile, a medium-priority task can preempt the low-priority task, which holds the resource. As a result, the medium-priority task executes while the low-priority task, holding the resource, and the high-priority task, blocked, are waiting. The high-priority task effectively waits until the medium-priority task completes and the low-priority task releases the resource.

Solutions to priority inversion:

• Priority Inheritance: When a low-priority task holds a resource needed by a high-priority task, it temporarily inherits the higher priority. After releasing the resource, its priority reverts to the original.
• Priority Ceiling Protocol: Each resource is assigned a "priority ceiling" — the highest priority among all tasks that may use this resource. A task can access the resource only if its current priority is higher than the ceiling of all currently occupied resources (including those it already holds).

In iOS, Grand Central Dispatch (GCD) and Operation Queues have mechanisms to minimize priority inversion, but in complex locking scenarios, such situations can still occur if used improperly.