For example, in the sequence late - on time - early, early is the antonym of late, and delayed would be a synonym. But what about on time, the "neutral" word in the sequence? What is the relationship of on time and early? Is there a word for this?
There are a lot of terms being used in your question. In an attempt to make things a little more clear:
The first thing to remember is that "opposite" here does not strictly mean "polar opposite on one particular scale." With regards to late, on-time and early are both antonyms.
The second thing to remember is that antonyms are not logical constructs — they are still linguistic constructs. The implication that two words are antonyms of each other is not inherently wrong but it may muddle the truth a bit. For instance: early and late are antonyms of on-time but it is entirely possible that the inverse is not as true. Is on-time really an antonym of early? Perhaps, but it causes me some pause.
In this case, the sequence is variance between arrival and scheduled arrival. The center of this sequence can be called many things:
And so on. Most of these words are used for a more strict definition of sequence or to explain a point between two distances.
In terms of looking at things as a sequence, the term antonym drastically shifts meaning since these things are much more logical or mathematical. Specifically, what is opposite depends a great deal on the type of sequence being used.
Unfortunately, the more picky one gets about opposites, the less the term antonym applies. If two towns are across the river from each other they are opposite each other but they are most certainly not antonyms of each other.
My dictionary is not doing this word justice, unfortunately. Neutral, in your usage, implies the halfway point you described from earlier. But in your example, on-time fulfills more of a pinnacle or balancing point:
The act of being late or early is missing the goal of being on-time. Represented as such, late and early are antonyms of on-time and could be considered opposites of each other in the same sense as the two towns across each other from the river.
Imagine a mathematical tree drawn out with the tip being on-time and the two children as late and early. A line connects late and early but only by traveling through on-time.
All of this is to lead into the actual answer to your question:
There are two ways to answer this question: One is to look at the relationship between on-time and early as they exist in a sequence and the second is to look at them as potential antonyms.
The difference between them with regards to the sequence is strictly one of numbers: on-time would be the goal and early is someone not hitting that on the nose.
In regards to them as potential antonyms, one could make the case of them being antonyms of each other.
The question you may have been trying to ask was:
The answer is that on-time is also an antonym.
You have the wrong picture in your head, namely, a straight line segment in which the antonyms are at the two ends.
The correct picture is that of a circle, with the top point removed, and the two antonyms pulled back just a bit. The “bottom” point is the “neutral” point. Then, whether you are dealing with synonyms or antonyms depends on your point of reference. The “naïve” point of reference is to simply consider the relationships of the surface meanings of the things at about the same hight on the circle, in which case, to use your example, “early” and “late” are antonyms. The “sophisticated” point of reference is to use the neutral (actually, not “neutral” but “desired”) point (at the bottom of the circle) as the point of reference, any and all deviations from which are considered SYNONYMS. That is, being too early or being too late are SYNONYMS in relation to being “on time”.
The case in point concerns time, and my take is that the term “on time” IS the term for the “neutral” / “desired” status between “early” and “late”.
In WordNet, these would fall under the more general category of