I actually wasn't able to guess from the method name what exactly it would do. Maybe something like withInterval() would be more intuitive, named after JavaScript's setInterval()

This doesn't run at an interval on its own. It only triggers as you pull values from the list, indicating that it's still running.

heartbeat is the standard term for this.

https://en.wikipedia.org/wiki/Heartbeat_(computing)

You give a very specific example. If a cache is used for locking, there is nothing wrong with reacquire of lock in the method every; it will not cause slowdown. If another locking mechanism is used, where the process of re-acquiring the lock is long, then this is an even more specific case and a separate example is needed.

This can also lead to misunderstanding when reading the code. When looking at code from the example, it may seem that heartbeat will really be called every 4 minutes. But php is a synchronous language, and if the report generation is long, the next callback call can be in 4.5 minutes or in 10 minutes, or in hour.

Framework should not have methods with such unpredictable behavior. For example takeUntilTimeout and throttle methods are more predictable, takeUntilTimeout takes new element until timeout reached but do not promises that processing will finish before timeout.

For your special case is enough to use tapEach or takeWhile methods with very simplie logic. This will be more readable and more flexible.

Reports::where('status', 'pending')
    ->lazy()
    ->tapEach(function () {
       if ($time >= $lockReacquireTime) {
          $lock->reacquire();
          $reacquireTime = now()->addMinutes(4);
       }
    })
    ->each($this->generateReport(...));