I'm more likely to think you have oil leaking in from your turbo. Also verify for us that your Turbo has a speed sensor; and if so clean it.
Your CAPS-2 system is a HPCR type. As such, it uses the same CAPS injection as as CAPS-1 system but, but in your CAPS-2 there is no STATOR or Fuel Distributor, because you have a common rail to deliver high pressure to so-called smarter injectors.
By smart, I mean your ECM controls the timing vs. in CAPS-1 the timing was controlled by the Stator and a rotating fuel distributor system to "dumb" injectors.
So if you don't have oil leaking into your turbo intake (which is only a 30% chance) then I would bet you have a stuck fuel injector which is more common with 2005-2006 RVs with a HPCR system. And since it's only smoking at idle, think you might get away with a Seafoam cleaning.
Note: Cummins replaced the HPCR in 2004-5 with a HPFR system in 2007 (RV models) and this type of system is still in use today.
Also, the HPCR lift pump (CAPS-2 system used in late 2004-6) is different than the early 2004 CAPS-1 lift pump system. Still, the only purpose of both lift pump types are "to start the engine." So if your engine starts and keeps running, which you say it does, then I would NOT be focused on the lift pump as the problem.
What color is the smoke? I assume it's black?
How many miles are on your engine?
Seafoam Tip: Fill a fuel filter with sea foam and start your engine. It will smoke a lot at first and then that white smoke will go way. ...And maybe, if you are lucky, all will be good again. ...And seafoam will not hurt your engine.
Tip #2: If that does not work, add Seafoam to your fuel and drive for 200+ miles.
Tip #3: You might also consider adding Seafoam to your engine oil just before an oil change. This is to clean the carbon off your piston rings among other things. Then drive under light loads for 100-150 miles, and then change your oil. It's all good preventative maintenance.
One last point: RV delivered in 2005-6... some owners find their fuel hoses are deteriorating due to USLD fuel eroding away the inside of the fuel lines, which seem be made out of a different material than those hosed used in 2004 and earlier. The problem is that with these 2005-6 hoses, the rubber inside breaks down and creates internal "flappers" that cause diesel fuel to "foam" and that causes problems with the HPCR pressure sensors.
One solution is to replace the fuel lines which is expensive and is a PITA. The other solution is to install a FASS or AIRDOG electric fuel pump; and I think the AirDog pump maybe a better way to go for your type of CAPS-2 pump, but I'm not sure about that.
Other than these fuel delivery concerns, the ISC/ISL is still a great engine.