"Do I" in past narrative tense

Consider the following made-up passage where "do I" is used to indicate internal monologue.

"And where were you on that night?", she asked. I hesitated. Did I lie, did I tell the truth? I wasn't sure I could lie convincingly, but telling the truth seemed more risky yet.

Compare to the same passage where "Do I" is kept in the present tense:

"And where were you on that night?", she asked. I hesitated. Do I lie, do I tell the truth? I wasn't sure I could lie convincingly, but telling the truth seemed more risky yet.

Which one is idiomatic? I know that past narrative tense forces all present verbs to shift to the past, but in this particular example, "Did I lie, did I tell the truth?" just somehow sounds... weird to me. Am I wrong?

(This question was triggered by seeing a variant of the first version, with "did", in a published novel, and being surprised by it. I'm not a native speaker)

That sentence is the narrator's internal narrative, describing their thoughts when deciding how to respond to the question. So even though you're describing something that happened in the past, the person's thoughts at that time were about the present of that time.

Therefore, you should use the present tense.

This relationship would be clearer if you wrote something like:

I hesitated and thought "Do I lie or do I tell the truth?"

"thought" is in the past, but the contents of the thought are in the present.

But in literary writing, it's common not to use quotations for the narrator's internal monologue.

"And where were you on that night?", she asked. I hesitated. Did I lie, did I tell the truth?

Further to Greybeard's answer, I would add a subtle point about using the simple (narrative) past. When I first read just this much, I did not take the did with the meaning of should as in "Should I lie?" (i.e., the historic present), but rather assumed it was narration, i.e. a small jump in time to after the response, as in "Did I in fact lie? For example, if the narrative had continued:

Did I lie, did I tell the truth? There is no transcript or tape of my interview. I remember saying "....," but the police insist I said "...."

Or, similar to Stuart F's comment: "You be the judge."

If an author realizes something can be misread, they should change it, even if the intended reading is a correct one. The reader shouldn't have to pause and reread to "discover" the the intended meaning. Such cases no doubt arise because the author doesn't see any ambiguity.

Did I lie, did I tell the truth?

This is the simple past and the default for narrative.

Do I lie, do I tell the truth?

This is the historic present tense. It is used as a device for adding immediacy to the writing.

Both are possible.

Short Answer

The use of the present tense in stream of consciousness is the norm. However, be careful in reading a text, as both of these passages are structurally idiomatic depending on context, where different texts convey different meanings, both of which are written in a grammatically standard way.

Long Answer

These two passages convey two different meanings both of which are standard English. While your quotations are stripped of context, both are grammatical:

Do

"And where were you on that night?", she asked. I hesitated. Do I lie, do I tell the truth? I wasn't sure I could lie convincingly, but telling the truth seemed more risky yet.

This is the standard way to use stream of consciousness to indicate present-tense thoughts. From the context of the short passage, it appears that the author wants to communicate that the character is trying to determine a course of action: should I or should I not tell a lie right now?

"And where were you on that night?", she asked. I hesitated (because I didn't want to be caught in a lie). Do I lie (to this question she just asked), do I tell the truth? I wasn't sure I could lie convincingly, but telling the truth seemed more risky yet.

In your hypothetical, the use of "do" would be the convention. This seems to be what you are asking about. When doing stream of consciousness, use the present tense for currently occuring events in the narrator's experience.

Did

"And where were you on that night?", she asked. I hesitated. Did I lie, did I tell the truth? I wasn't sure I could lie convincingly, but telling the truth seemed more risky yet.

In this passage, although it doesn't seem the intent of the author, it is possible for to use the past tense 'did' so that the narrator's inner monologue is seeking to recall a past action. If the character had other conversations with the interrogator, for example, then it is possible that using the past-tense did indicates the character searching out a prior decision. In other words, given the lack of context, this passage might be interpreted as "Did I tell a lie? Should I tell another if I can't recall what I said before?.

"And where were you on that night?", she asked. I hesitated (because I didn't want to be caught in a lie because of having already answered before). Did I lie (previously), did I tell the truth? I wasn't sure I could lie convincingly (right now), but telling the truth seemed more risky yet (given what I already had said).

The Preterite, Historical Present, and Stream of Consciousness

In narrative, these different grammatical devices are used to flesh out some details on the narrator's point of view, and to some extent, each is used to shift from the objective to the subjective. The simple past tense is generally used to convey the factuality of events.

Preterite

He told a lie.

Here, an author is essentially declaring that the narrative is true. The character in question did tell a lie, and the author wants you to believe he told a lie.

Historical Present

Had I told a lie, the character asked himself? He thought back to the conversation:

"Yes, I was there," I say. She now follows up looking for certainty.
"And you sure you were nowhere else?"
"Absolutely, I was there," I reiterate. Of course, I had been drinking, and maybe my confidence is simply to hide my embarrassment of being unsure because mother hates it when I drink.

Was it a lie? I had done my best to answer truthfully, vodka notwithstanding.

Notice how in this passage, the narrator takes the character into his historical thoughts as they were unfolding to interject the subjective nature of memories. There can be no doubt the character recalls the events as they unfolded, but those events DID happen in the past, so perhaps the intention at the moment was not to deceive about where the narrator was, but rather to cast doubt on the accuracy. If a lie is a communication with an intent to deceive, perhaps the claim was merely inaccurate. Even in the relative present, the character doesn't believe he tried to deceive and then recognizes that sometimes, decision-making and intention are not clear cut.

Stream of Consciousness

He thought back to what happened as drifted to sleep. He had told a lie. Unless, of course, his version of the events were a confabulation. Perhaps he did tell the truth. Who was to say what the difference between a lie and truth was anyway. As he drifted into sleep, both the idea that it was a truth and a lie gave way to darkness.

Here, an author uses the phenomenological nature of stream of consciousness to draw the character's own doubts out to warn the reader, in essence, that whether or not he told a lie isn't clearly established by the character.

Conclusion

Like all text, context is important in understanding meaning, but in the simplest case, using stream of consciousness means that the character uses the present tense to speak about the present and past to speak about the past. As literary devices, moving back and forth between the past, present, and future; shifting between the points of view of characters, and combining them can be used to draw into question the question of what exactly constitutes "reality", which often changes rapidly in a text depending on who and what are presented to the reader.

Very sophisticated authors often present competing realities and allow the reader to determine their own perspective, or intentionally try to conceal or mislead the reader leading to "ah-ha" moments to relieve dramatic suspense.