I'm not able to access the LSC forum anymore, but I know which fits you are talking about.
The Rifter, Tormentor, and Punisher are pretty standard solo/small-gang roaming ships. They work pretty well for the purpose, with the main drawback being that faction frigates are prevalent enough for them to generally be at a disadvantage unless they outnumber the adversary. It's a good idea to add recommended ships larger than frigates for solo/small gang roaming, though. Those tend to be nano ships. I'd point to Omen Navy Issue, Oracle (T2 pulse lasers are a must for both, I think WHC has fits that I'd go with for both), Osprey Navy Issue (like a Caracal but better), Orthrus as examples. I tend to be more interested in fleet doctrines so this is a little bit outside the area where I know most.
Taylor Moon's mention that if dual-prop is a priority, Thorax is a better choice than Omen is correct. That doctrine is specifically a dual-prop Thorax doctrine which works very well in Low-Sec engagements. It's a well-known doctrine which has been around for years. I wouldn't use those fits for kitchen sink or small gang roaming, but once you have the numbers to fill out a proper fleet, that's the first doctrine that I'd go for in Low-Sec (and my favorite T1 cruiser doctrine overall). I've seen more variation in the Celestis fit than anywhere else in the doctrine (mainly in what's in the high slots that gives it a secondary anti-tackle/anti-drone role: LSC forum has RLML, UniWiki has smartbombs, Pandemic Horde Inc. corp fittings version has LML).
I'm not a fan of the other doctrine. Taylor Moon is correct that it's based on RR Dominix (in fact, it does include Dominix as well as Armageddon). Spider tanking is a thing, but it generally doesn't work as well in the current meta as dedicated logi ships and dedicated damage ships, on top of the fact that both drone ships and battleships tend not to do very well in PVP situations nowadays, outside of niche situations that generally require ships which cost more than I would be comfortable with if I was responsible for Uni SRP. LSC's neighbors the UNF have used Armageddon fleets to defend their structures (although the armor timer fight that I joined them in a few days ago was Harbingers, to make it easier to work with the Villore Accords fleet that they got as backup), but the fit is focused on capacitor warfare entirely, without and cap-chaining or remote repairs. They bring dedicated logi with them instead. I would go with a Bhaalgorn instead (the cheapest of all faction battleships because of how many people farm Delve) because it has stronger neuting power and can be fit with bonused turrets while not being that much more expensive. I just don't think that a battleship doctrine is worth dealing with until LSC takes off a bit more. Even recognizing the reasons why E-Uni generally encourages its members to avoid using capital ships, it's probably better to arrange capital support for a fleet of T2 or faction cruisers or battlecruisers (I'd suggest something other than the long-range alpha HAC fleets that dominate the big Null meta, they don't necessarily work as well with the numbers that LSC is likely to have or the ranges of Low-Sec engagements).
While the drawbacks of battleships are such that the hulls which tend to be viable as fleet doctrines are almost always faction battleships (Machariels, in particular), if I was to go with a T1 battleship doctrine, it would be something like NSC's Maelstrom doctrine, to focus on high alpha damage.
This was the result of the only time that I know of that doctrine ever being undocked (also the only time that I remember BLAP Vexors being used, which was something like the second fleet that I was ever in). When I asked Urban about it a while later in LSC Slack after I had moved over there, he said something to the effect of "mistakes were made, FAX was dropped."
https://zkillboard.com/related/30045353/201905210100/
If LSC needs to form up a more expensive fleet than Thoraxes, the go-to doctrine should be something much cheaper than a battleship fleet. E-Uni uses the same Ferox fit that basically everyone in Null uses, but the numbers and range of Low-Sec engagements mean that I wouldn't really use that in Low-Sec. Autocannon Hurricanes would be my first pick (with one advantage being that they use most of the same support ships as Ferox and Caracal fleets, such as Ospreys), with Harbinger, Brutix, and artillery Hurricane all also being worth consideration. And if going beyond that, HACs and faction cruisers/battlecruisers are similar price to T1 battleships fully fit, but more versatile and can be used effectively with a lower SP investment than it takes to use battleships effectively. Hurricane Fleet Issue, Gila, Sacrilege, Drekavac, BNI, HNI are all reasonable candidates that see some amount of use. I've had the idea to run dual-prop Deimos/Vigilant with T2 logi in the same way that the Thorax doctrine, but I've never seen this actually implemented.
Shauny, feel free to discuss this with me further.