While not outright stated as a justification, this can be inferred from the description given in the monster manual:
Skeletons have traits like Obedient Servant which indicates that they mindlessly follow orders and Habitual Behaviour which states that in the absence of orders they have a tendency to follow routines resembling their behaviour in life. Both of these point towards a lawful nature, i.e. they behave in a predictable, orderly fashion. The same description also provides a justification for evil as they're driven towards killing living things on sight. Of note is that Skeletons are explicitly pointed out as not mindless:
Although they lack the intellect they possessed in life, skeletons aren't mindless.
—Monster Manual pg. 272
Their reasoning ability is limited compared to the average living human, and while only capable of interpreting verbal commands literally they are nevertheless stated as being capable of complex reasoning.
Zombies are also servants created from necromantic magic (either environmental or cast by a necromancer) obviously, but there's a slight difference in ability: A zombie truly is mindless. It has no inherent instincts or reasoning capabilities beyond identifying and attacking threats to the point it is not even capable of avoiding harm. A zombie currently not attacking a target or carrying out an explicit order (it is stated they are not capable of understanding anything much more complicated than "go in that direction and kill") doesn't have an inherent motivation to do anything much at all. Presumably its this complete lack of reasoning that makes it neither lawful or chaotic; If the magic animating it wasn't itself considered evil it would probably be considered neutral.
Of course as you note alignment is to no small extent a matter of opinion, but I believe this is most likely the reason for the difference in this particular case.