So far I don't see a reason why LR could fly them, or any other non-Omicron faction, especially Lane Hackers, Bundschuh and Hessians
In Vanilla, LR sold the Dagger, Bundies sold the Stiletto, Outcasts and Hessians sold the Sabre, and Lane Hackers sold the Dromedary. So only one out of three "omicron" ships is actually sold by an Omicron Faction.
All those factions have just as much right to fly a Borderworld ship as the Outcasts do. Your opinion of it being an Omicron Faction only ship is false, since all historical evidence points them to being flown by predominately non-omicron factions.
Edit: For more technical stuff, Omicrons are technically Edge Worlds, while Taus, Omegas and Sigmas are Border Worlds. So maybe only the Hessians and Bundies should be flying those ships?:)