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I think it it possible to say "Завтра я обедаю с ним" in order to express I (will) have dinner with him tomorrow.
<Future action by using the imperfective present>
But it is not possible to say "Через два дня я бедал с ним" in order to express I was going to have dinner with him two days later <future action at the past point by using the imperfective past>, because this sentence just expresses the fact (not plan) I had dinner with him two days later.
Is my understanding OK?
Завтра я обедаю с ним - to express future is fine.
Через два дня я обедал с ним - can be used to describe sequence of the events in the past, which could imply a future action during the narrative.
Example:
It happened unexpectedly. I met him first at the port where he worked. I had dinner with him two days later. -
Это случилось неожиданно. Сначала я встретил его в порту, где он работал. Через два дня я обедал с ним.
Yes. And your sentence "I was going to have dinner with him two days later" is better translated as
Через два дня я должен был (по)обедать с ним.
or
Через два дня я собирался (по)обедать с ним.
or
Через два мне предстояло (по)обедать с ним.
And I have put (по)обедать because either imperfective or perfective works fine, but it depends on some nuances. If you want to emphasize some details of the activity (i.e. having lunch with him): what you were going to eat, what you were planning to discuss at lunch, what clothes you decided to wear for the event etc., then only imperfective is used.
If you emphasize the fact itself, then perfective is preferable, but the imperfective is still possible as it seems to me. But it's a very subtle nuance.