I may need some help here - but I will try to give you what you need.
LR
In the Print module under Print Job I have tried 2 main ways of printing - i will explain both and the result I get (I will not go into the areas of Image Settings, Layout and Overlays as I believe they have no bearing on my problem).
Processs 1
1. Draft mode - not ticked
2. Print Resolution - 24'ppi
2. Print sharpening - ticked and medium
4. Profile - Managed by Printer
5. Rendering Intent: Perceptual (but i have tried all 4 and there in no significant difference)
6. Then selecting Page Setup or Print Settings - the same popup screen called Print Setup is displayed (makes no difference which button I press at this point).
7. Under the popup screen (Print Setup) I select the printer (Canon iP42''), paper size and source and orientation. I also click on the Properties button and another popup screen (Canon iP42'' Properties) is presented.
8. Under the popup screen (Canon iP42'' Properties) there are a number of tabs:
9. Under Main I select paper type (I am using Canon Photo Paper Plus Glossy). Print Quality = High. Colour/Intensity = Auto
1'. Under the other Tabs (Page Setup, Effects, Profiles and Maintenance) I don't usually touch these unless to reconfirm page size and layout under the Page setup tab.
11. I then OK out of these screens, click on the Print button in LR and click on OK to print.
12. The printed image is very unsaturated.
Processs 2 (is the same as above but with the following difference)
4. Profile - Canon ip42'SP4 (I have also tried Canon ip42'SP2) both give similar results)
12. The printed image is extremely saturated.
Photoshop
I am working in RGB: sRGB IEC61966-2 (don't know it that is relivent?).
To Print I have tried 2 different approaches of either letting Photoshop determine colours or my printer, both give similar results, but I usually select my printer option.
Here is the process for selecting Let Photoshop determine colour:
1. I select - Print with preview.
2. Under Colour managment Proof = Document.
3. Let Photoshop determine colour
4. Print Profile is automatically selected as Workin RGB: sRGB IEC61966-2
5. Rendering - I leave at Perceptual
6. I set the position and scale as needed.
7. Then I click on Page setup.
8. A Page Setup popup screen and I set the paper size and orintation and then click on the Printer button.
9. Another Page Setup popup screeb appears - this time the same as LR - I then follow steps 7 to 1' as listed unter LR (ist the same process)
1'. I then OK out of these screens, click on the Print button in Photoshop Print popup screen and then I click on OK to print.
Here is the process for selecting Let Printer determine colour:
1. I select - Print with preview.
2. Under Colour managment Proof = Document.
3. Let Printer determine colour
4. Print Profile is greyed out (disabled)
5. Rendering - I leave at Perceptual
6. The rest is all the same as point 6 to 1' above for letting Photoshop determine colour.
I hope this is what you needed to know.