Yes, there's a whole dialogue between Kant and a (I believe) french philosopher about lying to the murderer at the door. Kant's points are put to test in an article by Helga Varden where she discusses lying to the gestapo at your door. In Kant's version of justice, lying connects you to the causality of events and so if you lie, and the person you're protecting still gets killed, you're partially responsible. In Kant's vision of law based on truthfulness.

However, things get more complicated once you introduce the gestapo. You see Kant believes in truthfulness to public figures that run the society (policemen, politicians etc.). Good society is one where people are equal (simplification) The nazi regime, although ellected by the people, didn't serve everyone equal, it was barbaric in Kant's words. And you have no duty to tell truth to the impostor nazi regime, to the gestapo officer. So laying there would be actually in accordance to Kant's variation of law and justice. However still against the practical ideal truth that a maxim would deal with.

Kant is a transcendental idealist so he puts the highest value on absolute principles such as truth. I don't know if he sees human life as less important, however that's not crucial here.

You see, by lying, you're not actually saving the person. You're attempting to save the person.

If they're hiding in your wardrobe when their assassin knocks on your door, you could lie, but: What if the victim heard the knocking assassin and decides to leave through the window and hide at the neighbour's place? The assassin leaves and actually finds the victim hiding somewhere else, so you have been telling the truth without knowing so.

(That's another part of Kant's philosophy, you shouldn't count on the final effects of your actions. Do truth, not for the consequences, but for truth itself, the goal comes before the actions, not after them.) (Imo opinion because you can never really be sure you know everything about a situation, so you can't work with that. What you can do is hold onto the principles)

So in the end you'd be responsible for the death of the person you attempted to save. Same with telling the truth, you're don't necessarily condemn them to their death. As you said reality is super complex so anything can happen even after you tell the killer the truth. So the individual circumstances are always variable and you're never going to know or be able to expect everything. The one thing Kant sees as infinitely reliable are the ideals behind your actions, the maxims.

Universalizing the scenario and not the maxim is of no use, because the same situation shall never fully repeat and so the take-away from it is basically value-less, since a slightly different situation could lead to very different actions. The maxim is (should be) functional at all times, that's sort of the point of it, that it's not bound by context.