Fort Zombie is the best suggestion I can make. It's the most similar game I've seen mechanically, since it has some recruitment, base management, character advancement, sending out a raiding party, assigning tasks day by day. The term "raiding party", which I appropriated in my own zombie game inspired by LCS, is a nod to Fort Zombie. I often wondered, when playing Fort Zombie, if the developers had played LCS and taken inspiration from it.
Red Faction: Guerrilla also comes to mind. It's in a completely different genre; it's a third-person open-world action game, and is very very light on its strategy and RPG elements. I'm not entirely sure why my intuition says it fits here, given how distant it looks on paper. But I know when I played it I was very impressed by the game, thought its shrewd design was underrated, and also wondered if any of the designers had taken any inspiration from LCS.
For a more real-world setting, the old Gangsters: Organized Crime is pretty similar, and I've seen a couple comparisons between it and LCS. It's set in prohibition era, you play as a mafia family, and it's more on the strategy end. Lots of emphasis on business fronts, safehouses, bribing police, rivalries between crime families.
Finally, if you're most interested in the RPG side of the game, Liberal Crime Squad is based on Oubliette, which is one of the foundational games among computer RPGs. I believe the early Wizardry games, which were also inspired greatly by Oubliette, are pretty similar to the RPG and dungeon crawling side of Liberal Crime Squad. They're both fantasy games, though.