WARNING: LowSec is a dangerous place to leave Assets hanging in space. This is not intended for a beginner in EVE Online, as you can and will lose your stuff in LowSec if you are not prepared. Take all necessary precautions when attempting to do the following!
Running a POS in LowSec takes some preparation and planning, but it can be done by a careful player and is very rewarding.
What do you get from a LowSec POS? Most people will point out the private research slots and the bonuses to research and production which are a huge advantage for the research of "big stuff" or copying blueprints. But there is more: LowSec POSes additionally give you the opportunity to get moon minerals and react them as well as booster production, which is similar. Here is a POS setup that allows a large variety of operations in space < 0.4:
Gallente Control Tower, Large:
1 x Assembly Array - Component
1 x Corporate Hangar Array
2 x EW - Stasis Webification Battery
2 x EW - Warp Disruption Battery
2 x Mobile Laboratory
1 x Moon Harvesting Array
1 x Reactor Array - Simple
2 x Shield Hardener - Explosion Dampening
2 x Shield Hardener - Heat Dissipation
2 x Shield Hardener - Photon Scattering
3 x Silo
3 x Turret - Hybrid - Railgun, Large
4 x Turret - Hybrid - Railgun, Medium
1 x Turret - Hybrid - Railgun, Small
These are only the modules that are Online, with additional offline modules you can switch out production types or lower/raise defenses as you think it's needed.
Your numbers will vary from here on, so please run your own math and note that I'm assuming 30 day cycles (a "month"). I'm also only using thumb figures, really: Run your own math and you'll see that I'm using rather conservative figures.
A setup like this costs around 900M including Ammo and Strontium for timing in case of an attack. It also requires 28,800 Fuel Blocks every 30 days for fueling which comes to around 450M/month.
It gives you access to 6 ME / 6 PE / 2 Copy Slots / 10 Invention Slots, produces 72.000 Units of Moon Mineral and can use a simple reaction yielding 144.000 Units of reacted materials.
Assuming a low grade moon mineral at 5000 ISK per Unit generates 360M ISK and requires you hauling stuff only a couple of times a month. Let's also assume the reaction we can do is for Prometium, which requires Cadmium and Promethium. This will cost 504M for one month and yield Prometium worth 835M giving a plus of 331M. It requires action 4 times a month to haul input/outputs from station to POS. Effectively, this tower, simply by running the reaction and the moon harvesting, brings in 241M a month so it has paid for itself within 4 months. Add to that production profits and research makes it well worth having something like this.
But there is a problem: Logistics. It's no good to set up something like this without getting your stuff there and back to a trade hub. Cloaky haulers can work but require more effort, and not everyone has a Jump Freighter. Enter: The Hauling Services of New Eden. Assuming you contract stuff in and out only once a month from a nearby system you can get your stuff from HiSec to the LowSec station of your choice for around 120M per round trip. Even then you would be up 121M and still had access to all the other features of the POS.
Of course this all assumes you didn't disturb any locals that consider the system you live in "theirs". That's why I'd recommend getting to know the system and its residents. There are many LowSec system to set up a POS, just find a quiet system with a station and production facilities if your plan requires them and keep a low profile. People will blow up your assets because they consider you an invader to their home.
You can also run two simple reactions on a POS which is a bit more risky because you need to offline defenses, but with smart selection of the reactions you are running you can easily make a PLEX worth of profit from a POS like this.
Summary: A LowSec POS can be a valuable asset for any player, can be set up to be cost neutral, and brings a lot of variety of play styles onto the grid.