So may things wrong.
The rifle should be cleaned (including scrubbing the chamber with a chamber brush and CLP by hand) , and the upper receiver bearing surfaces lubed with a fresh coat of CLP before the rifle is every shot (and during cleanings between outings as well).
Hence CLP had a cleaning agent in it, so it works not only to begin with to remove the assembly grease and debris, but as a great lube as well since it will break down any fouling before it has the chance to collect and choke the rifle out.
Next, once you have done the above, the rifle will need to be broken in with full power brass case ammo. The reason for this is that the inner surfaces are still new/rough from the new parkerizing/anodizing coatings, and these need to semi polish out through live fire of the parts working against them self. And, Cue in the CLP with it cleaning agent, since it will make sure that as these surfaces mate in to created a powderized fouling, end up with the fouling flushed away as well.
So on that note, large can of BreakfreeCLP to give the rifle a good cleaning to flush away all the Grease and not cleaning lubes that where used (including scrubbing the chamber with a Chamber brush and CLP by hand) and once all the fouled CLP has been wiped away, then a fresh coat of CLP on the bearing surfaces next. As for ammo, Win White box, 233 brass case 55gr is a perfect ammo to use for the first 100 rounds to allow the rifle to break in/self polish out. It"s not going to lay down any bench rest type groups, but is has enough power and reliable enough to use as break-in ammo.
As for the only other solvent to use on the rifle besides CLP, and that is something to clean the actual bore of the barrel. Here, the trick it to use something that will not have an adverse effect with the CLP (Hoppes cleaning solvent leaves behind a resudue that the CLP turns into a worse sticky mess) and something like Sweets copper solvent is used to clean the bore instead.
So cleaning and lubing of the rifle breaks down like this,
The barrel bore is first cleaned with Sweets, since it will not take a lot of scrubbing to remove the copper from the barrel. Clean/dry patches are pushed down the barrel from the chamber to the muzzle until the bore is dry, then CLP is used with a chamber brush by hand to clean the fouling out of the chamber and barrel extension void, then a quick shot of fresh CLP shot into the chamber, Q tips used to clean the barrel extension void area, then the fouling from the chamber is pushed down the barrel and out of chamber with dry patches next. The reason that you clean the bore, then chamber next, is Sweets leave behind not protective coating in the bore, and when you go to push all the fouled CLP out of the chamber through the bore, even with the chamber apprearing to be bone dry, there is still enough CLP remnants in both for short term storage to prevent rusting.
As for the rest of the rifle, including the buffer, the buffer spring, and even the inside of the receiver extension, CLP only. Here, just think of this cleaning as just changing the oil in the rig. As for the B/C, if you pull it down to a cleaning level, give the parts a quick coat of CLP before you start to clean the barrel, buy the time you come back to clean them, the fouling will wipe off isntead.
As for lubing the bearing areas of the upper receiver, it's very, very simple to do. The buffer and spring get a light coat of CLP before they are installed, then with the B/C reassembled and it having a light coat of CLP inside and out, it put back into the upper receiver, the rifle dry cycled a few times to migrate the CLP from it to the upper receiver surface ,and now the rifle has been lubed and ready to go.
Lastly, the wet part of CLP is mostly the cleaning agent (very small part of the wet is a rust protection coating that works even when the lubed parts look dry), while the Dry part of CLP (Teflon suspended in it), is the lube part of CLP. So the how theory that CLP dies to fast and is not lubing the rifle, is nonsense.