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This is a mistake, perhaps the result of hypercorrection on the part of the writer.

As the object of the preposition for, the pronoun I should actually be me.

A grammatically correct version of the sentence would read as:

And in order for you, me, or any other end user to access the database engine, we need to go through some sort of database application.

Here, some means

some
1. being an undetermined or unspecified one

So there isn't an issue regarding plurality: justification can be singular.

You can use justification as a plural like you would with good reason.

Here is an example in the same sense as your example. I don't know why there were budget cuts. There must be some good reason for the recent budget cuts →

1. There must be some justification for the recent budget cuts.

There can also be multiple undetermined justifications. I don't know why there were budget cuts. There must be some good reasons for the recent budget cuts →

2. There must be some justifications for the recent budget cuts.

If there is just one justification for a particular action, then justification (singular) is correct.

3. We have just one justification for the recent budget cuts.

If there are more than one reasons for a particular action, then justifications (plural) is correct. For example, imagine that there are ten reasons for the budget cuts, but only three are presented: here are some reasons for the recent budget cuts→

4. Here are some justifications for the recent budget cuts.

Here's a headline I found online that uses justifications.

18 Solid Justifications for Cloud Computing -- and 10 Situations Where It Doesn't Work