First things first, what power are you wanting to gain?
I would do a compression test, then do a leak down test out your valves and crankcase itself. Next, you will need to upgrade your pistons, connecting rods, crankshaft, bearings, and fuel system. I know ZZP offers a supercharger kit for the LS, but you will need to have these mentioned above out of forged metals, cast iron will not hold down the increased pressures of forced induction. The reason why I am urging to upgrade your internals first, MP81 on this forum had an LS Supercharged Eaton M62 kit, connecting rods and bearings were giving him rod knock after 8k mileage.
Next, you will need to upgrade your braking efficiency to slow down the increased power, its not vital, but its important to slow you down. I would also upgrade your drivetrain (axles are vital) to lay the correct torque down to the wheels, or you will be rebuilding them roughly twice a year. Also to add, upgrade your fuel system consists of 43lb injectors, drain the entire fuel system for 91/93 octane, which will be required for forced induction/high compression engines.
I would also upgrade your transmission, if its an automatic, you should be ok, but a manual will require a stronger clutch disc for power on/off through the input shaft.
You can also upgrade wheels/tires to lay it down if you are still rolling stocks, I would also upgrade your suspension for traveling with a full FE5 strut/spring combo.
This maybe to get very expensive, but the technician/mechanic gurus will not argue against this setup. You most likely would save more money selling your LS and buying an SS.
2009 Cobalt LS XFE U74
Mods: K&N Typhoon Intake, Option Cat-Back Exhaust, Cosmo Short shifter, Maxxim Ahead 17X7's, MPx shorty antenna, FE5 Strut/shocks, Tein S Techs, Moog endlinks, Moog spring seaters, ZZP shorty header, LSJ downpipe, LNF front grille