RAW different sources of obscurement don't stack
Nothing in the rules says that having multiple things that cause an area to be considered lightly obscured make it considered to be heavily obscured.
In a lightly obscured area, such as dim light, patchy fog, or moderate foliage, creatures have disadvantage on Wisdom (Perception) checks that rely on sight.
So, for example if you were to have foliage in a place and also dim light that would not make that space heavily obscured according to the rules, because heavily obscured has a specific definition of its own.
A heavily obscured area--such as darkness, opaque fog, or dense foliage--blocks vision entirely.
In your specific example, the character with darkvision will see in an area of low light as if it were lightly obscured.
There are simply no mechanics in the rules that say how that this would happen and, if so, how it would work.
Having the fog which also causes it to be lightly obscured does not cause it to be considered to be heavily obscured for that character. For that to happen you would have to have something that would cause the character to not be able to see that area at all.
DM rulings apply here naturally
Now, the rules don't specifically say that stacking different sources of obscurement is not allowed and thus it is well within the power of a DM to say that having enough sources of obscurement might indeed add up to an effect that counts as heavily obscured. In fact, the determination of obscurement is largely placed in their hands anyways since it is only very loosely defined in the rules.
Thus, this could be a reasonable ruling, but it will vary from table to table what the DM wants to counts as "obscured enough" to bump an effect up to heavily obscured.