It is definitely hard to survive in LCS. And unlike most games, it doesn't go out of its way to tame the authority figures in the game to make it easier on you -- even a liberal in heavy body armor with a machine gun is likely to get killed if they walk in and try to attack a police station. In "losing in fun" style, I actually fully intended that the first time you see a Police SWAT raid, you'll experience a full wipe and probably lose the game at that point. Fortunately, once you're anticipating it, there are multiple things you can do to try to avoid it happening again.
I'm a little rusty, as I haven't played in awhile, but from my point of view, most to least important when it comes to protecting yourself from raids:
1. Ensure you don't lose given a catastrophic wipe. Sometimes it's the police, sometimes it's worse. You can always surrender to the police, and they'll drag your people off and give them a fair trial. But you can't surrender to a torch and pitchfork mob, or a shady out-of-jurisdiction raid by the MIB. To that end, you might consider keeping your forces split into different safehouses, to ensure part of the LCS will survive at all times. Your founder is a particularly sensitive target, as the LCS will crumble without him or her; best not to have them in with the people you think are racking up the most heat. Try to get someone that is reporting directly to the founder and has a lot of juice, that is based in another safehouse. Worse case scenario, this lieutenant can still take over leadership of the LCS in the event of the founder's death.
2. Avoid a catastrophic wipe when raids occur. You can keep a small army around, but it takes a very large amount of firepower to fight off even an early police raid. Other options include surrendering, and either springing them from the courthouse, or fighting your battles in court with a lawyer; worst case scenario, your people end up with life in prison or death row, and even then you can always take anyone that's still free and attack the prison to release them before their execution. Court battles are much more survivable if you get a sleeper lawyer first... just make sure you have enough to pay the tiny nominal fee the sleeper demands to make it look "legitimate". If are hell-bent on fighting it out in the hallways of your safehouse, the least you can do is fortify the compound first. Security cameras will ensure you can look at the map and see all enemy units at all times, and booby traps will weaken and immobilize a proportion of the enemies. Finally, if the enemy is too strong, you can always walk up to some police and talk to them to give up, or simply dash for the exit, ignoring your enemies and fleeing in the direction of the exit in every encounter. Keeping someone trained in first aid in your party, like a nurse or doctor, will help to keep people from bleeding to death as you run for the exit.
3. Minimize the chance of getting raided in the first place. Keep your people divided up into small groups, and use unsuspicious safehouses. A team of three alone in a nice, respectable apartment in the upper-class part of town is much less likely to be raided than two dozen people trying to run an insurgency out of the homeless shelter. Installing business fronts in your upgradable safehouses won't prevent raids on those safehouses, but they will significantly decrease the frequency of them. The more sleepers you get in the police station -- whether cops or janitors, just people who work there -- the more likely one of them will find out about an imminent raid and tip you off in time to have the place be empty when the SWAT trucks show up. No special orders necessary, just having them in place is enough. And this may be obvious, but if you've been torturing some poor Conservative fast food worker the back room of the homeless shelter, get out of there immediately if the fast food worker escapes to tell his 50 closest police friends about the harrowing experience.
IIRC, the CCS won't enter the stage until a bit later in the game. They start appearing when you're doing well and Conservative reactionaries decide to take matters into their own hands.