The normal LS problem is coils. The identification of which coil is not always right, and usually several of them will fail within months of each other. The solution is to replace all the coils at once. If you had searched and/or read the stickys, you'd already know this and wouldn't have had to wait for a response.
When you replace a coil, you always have to replace the associated spark plug. Bad coil damages spark plug. Damaged spark plug damages new coil. Cycle repeats. It may have been coil 3, but it you didn't replace the spark plug, then new coil may be bad now too.
With the V6, there are known issues with the PCV valve plumbing. You should replace it all while you have the top half of the manifold off. It can also cause rough running and misfires. Searching would reveal this too.
If anyone has messed with the fuel injectors, the latches on the connectors may be broken and could also be causing your problems.
You'll get better help if you post the exact five-character OBDII codes.