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Have you got the most recent colormunki or an older model ? The latest should work on any monitor so long as it can run the software. However, a lesson I learned years ago is that even when a monitor is correctly profiled and displaying colours and tones as accurately as possible, it may not have the colour gamut that you want or expect it to have. In that case the results can still be problematic and you will see a difference between the laptop and the desktop screens, but it would be even worse without profiling.
I don't know how good the screens on those laptops are.
Profiling and Calibration are technically two different things. It is common with laptops to easily alter the screen brightness and thus ruin the calibration for which the profile was done. Be sure to note the brightness setting so that you can restore it when viewing photos in Lr. Also you might find that the brightness is changed in steps that are a bit big and that you may not be able to get the brightness you want. You might have to settle for something darker or brighter than your preferred target value.