I understand that with each LOINC code units given are just examples. Can someone please point me to the exact LOINC recommendation if the same code is to be used for different units within the same property.

For instance:

mg/uL, Kg/L, mg/dL, g/dL >> Mass/Volume

If these are the units of reporting, should we be using the same LOINC code (given that scale is changing across units and is not the same as that in the example unit)

If they’re all reporting the same thing (Mass/Volume) then switching from one unit of measurement to another is a simple transformation of the actual values. There’s no reason to use a different LOINC code just for different units of measurement when the property being reported remains the same.

As Christopher already stated, it shouldn’t matter, as switching from one unit to another is just a matter of a simple transformation.
When using UCUM notation (highly recommended) this can even easily be automated as there is a RESTful web service from the NLM available for doing so. See: https://ucum.nlm.nih.gov/ucum-service.html.

Well this may not always be so easy. Information systems have check the UCUM notation of the units. For blood gas parameters like pO2 and pCO2 (mmHg of kPa) the difference is not a factor 10 but 7.5 (or 0,133 the otherway around). Systems need to check the units received. notation have to be proper UCUM notation otherwise such a check will fail.

“Notation have to be proper UCUM notation, otherwise such a check will fail” …
Yes indeed! That is why lab systems should use UCUM unit notation all the way - everything else is doomed to cause problems.
BTW, UCUM notation for “mmHg” is “mm[Hg]”.