If you set the sigevent argument in the lio_listio() call, you will be notified with a signal (or function call) when all the jobs in that one particular call completes. You would still need to:
wait until you receive as many notifications as you have made lio_listio() calls, to know when they're all done.
use some safe mechanism to communicate from your signal handler to your main thread, probably via a global variable (to be portable).
If you're on linux, I would recommend tying an eventfd to your sigevent instead and wait on that. That's a lot more flexible since you don't need to involve signal handlers. On BSD (but not Mac OS), you can wait on aiocbs using kqueue and on solaris/illumos you can use a port to get notified of aiocb completions.
Here's an example of how to use eventfds on linux:
As a side note, I would use caution when issuing jobs with lio_listio. You're not guaranteed that it supports taking more than 2 jobs, and some systems have very low limits of how many you can issue at a time. Default on Mac OS for instance is 16. This limit may be defined as the AIO_LISTIO_MAX macro, but it isn't necessarily. In which case you need to call sysconf(_SC_AIO_LISTIO_MAX) (see docs). For details, see the lio_listio documentation.
You should at least check error conditions from your lio_listio() call.
Also, your solution of using a mutex is sub-optimal, since you will synchronize each loop in the for loop, and just run one at a time (unless it's a recursive mutex, but in that case its state could be corrupt if your signal handler happens to land on a different thread).
A more appropriate primitive may be a semaphore, which is released in the handler, and then (after your for loop) acquired the same number of times as you looped, calling lio_listio(). But, I would still recommend an eventfd if it's OK to be linux specific.