If you live in North America, there is probably already a lacewing there. It looks like the commercial lacewing is one of the
native varieties, so I would be comfortable ordering more to increase the population.
I think it's the ladybugs and preying mantis that are questionable as these things go. The ladybugs don't usually stay on the property they are released on. If I remember properly, there's also something controversial about how they're gathered. The preying mantis is usually a nonnative Asian species that outcompetes our natives.
I think you need to deal with the ants before the beneficial insects can deal with your aphids. The ants actively defend their
milk herds from predatory insects. You might try
Bryant Redhawk's technique of watering in fresh
coffee grounds on top of any fire ant mounds you find. If you can afford
enough coffee, maybe you can even make moats to surround the most important plants.