Would Kant identify the act of lying with the intention to delude or with the act of speaking untruth, when their conjunction is not given? It is possible to try to deceive someone but nonetheless impart truthful information to them. It is also possible to speak untruth without intending to deceive. When the intention to deceive + the act of speaking untruth = we have a clear-cut case of lying. However, what about the cases where we consider each conjunct separately?
This is a quite difficult question because Kant, so far as I know, never offers a definition of lying. But we can draw some contrasts that help make clearer Kant's understanding of the nature of lying.
Lying is not simply making a false statement
Truth means for Kant the agreement between facts and the proposition about them. The agreement between these is established through a logical judgment. Now it is Kant's opinion that nobody is ever able to guarantee that what he asserts is actually in agreement with the facts. The possibility of error cannot be excluded, since the proposition and the facts are not immediately related to one another but are related by the means of a judgment. Does it not seem absurd to require someone always to tell the truth, knowing that there is no chance that he always knows the truth. (Heimo E. M. Hofmeister, 'Truth and Truthfulness: A Reply to Dr. Schwarz', Ethics, Vol. 82, No. 3 (Apr., 1972), pp. 262-267 : 263-4.)
So telling a lie cannot be a mere failure to assert what is actually in agreement with the facts - merely making a false statement.
Lying is not merely deception
"I may, for instance, wish people to think that I am off on a journey, and so I pack my luggage; people draw the conclusion I want them to draw . . ." But although I thus succeed in deceiving them, Kant insists, "I have not lied to them, for I have not stated that I am expressing my opinion." ( Roderick M. Chisholm and Thomas D. Feehan, 'The Intent to Deceive', The Journal of Philosophy, Vol. 74, No. 3 (Mar., 1977), pp. 143-159 : 149. [Kantian quotation : Lectures on Ethics (New York: Harper & Row, 1963), p. 224.]
Although 'The Lectures on Ethics' is a pre-Critical text, I know of nothing in Kant's Critical philosophy that indicates a repudiation of this view.
Lying is an assertion intended to deceive
'I have not stated that I am expressing my opinion' (Chisholm and Feehan above). This gives us the essential clue, I believe. Let's follow Chisholm and Feehan a bit further :
What distinguishes lying as such from the other types of intended deception is the fact that, in telling the lie, the liar "gives an indication that he is expressing his own opinion." And he does this in a special way-by getting his victim to place his faith in him. The sense of 'say', therefore, in which the liar may be said to "intend to say what is false" is that of 'to assert'.
While Chisholm and Feehan are not expounding Kant's views as commentators, they do appear to me to produce a formulation of lying that fits Kant's examples. It fits the famous example of lying to the murderer at the door (Kant, On a Supposed Right to Lie). It is also perfectly in line with Kant's proscription against making a lying promise in the Groundwork (Kant, Groundwork of the Metaphysics of Morals, tr. M. Gregor, Cambridge : CUP,2012 : 15.)
The moral of all this ?
Kant's conceptualisation of lying, his understanding of the nature of a lie, contains nothing radically new. This should not surprise us since Kant aims to capture - to respect - ordinary moral thinking. Producing a fresh conceptualisation of lying would not be faithful to this enterprise of elaborating a moral theory that accommodates common moral experience. Kant's depth and originality as a moral theorist do not rest on his revising the concepts we use, such as lying, but in placing them in the radically new context of an a priori moral theory.