How long the Hitbox lasts/duration of the single hitbox also does not matter for SDI.
The difference is that the latter Lucario hits with the first hit of Dair, the smaller of a window he will be open at later in the move.
If I get hit on frame 4, I go into the phase where I am able to SDI. I do so the best I can. Now time passes and I cannot SDI any further. I am about to experience hitstun, and Lucario is about to continue with his attack. Let's just say that for the sake of argument and to demonstrate my answer better, let's just say that at the end of that all, Lucario is open for 10 frames exactly and that I experience exactly 10 frames of hitstun. Meaning the other person recovers 10 frames sooner from the first hit than Lucario recovers from the entire move.
Now, say that instead of frame 4, I enter the Dair hitbox later, say frame 7. The same thing happens here. I get hit, go through the SDI phase, it ends/hitstun is about to start/Lucario is about to continue with his attack. The difference in this scenario compared to the earlier one is that at the end of it, instead of having a 10 frame "advantage" against Lucario, it will be less. I will experience the same about of hitstun, I just am hit with the attack later. So I get hit on frame 7, experience 10 frames of hitstun, and then I can hit you. Naturally that means if I had a 10 frame advantage, it's now down to 7 frames (Being hit on Frame 4 vs Frame 7, I have 3 frames less to hit you).
Duration of a hitbox Generally does not affect SDI windows, neither does it usually affect the possibility of the opponent punishing (there are few instances where the opponent gets hit with the "later" part of a hitbox and because of that they barely miss the opportunity to punish the opponent with SDI/follow up attack because as you probably know, individual hitboxes rarely last for more than a few frames before disappearing.)
So in short, being hit by the later part of the first hitbox of Dair GENERALLY does not shorten Lucario's frame disadvantage enough for Lucario to avoid being punished by his opponent if they SDI outside the range of the second hitbox. I say generally because I've not looked at every character and seen whether that 3ish frame difference makes a difference in whether they are able to punish or not. That and while earlier I assumed for the sake of argument that the punishment Window was 10 frames, I do not know exactly how big of a window it is. I think it's safe to say it's at least 10 frames since I know moves slightly under 10 frames look easily guaranteed to hit on Lucario (Wario's Uair for example is definitely guaranteed.)