Good question. Per the notes from the Net Bible below, there are several possible explanations. I would add that what we have in Genesis is surely only a summary of God's interactions with Adam and Eve and it is reasonable to assume God may have made Himself clear in other ways as well. Moreover, even if Adam and Eve did not fully understand what God meant, that is not the same as God lying. Think of when we warn a child of danger like burning their hand on the stove, the child cannot understand fully if they have never been burned - they must trust their parent's judgment.
given that they were immortal as long as they ate of the tree of life, the meaning here could be that they would become mortal if they disobeyed God. This could be true even if the literal meaning of the words was that they would die immediately - not all language is literal. For example, in English, "Mom is going to kill you" can simply mean "You're in big trouble". Hebrew is an ancient language so we must be careful when drawing these types of conclusions from the English text.
God had mercy and extended their lives
Net Bible Notes - https://netbible.org/bible/Genesis+2
Or “in the very day, as soon as.” If one understands the expression to have this more precise meaning, then the following narrative presents a problem, for the man does not die physically as soon as he eats from the tree. In this case one may argue that spiritual death is in view. If physical death is in view here, there are two options to explain the following narrative: (1) The following phrase “You will surely die” concerns mortality which ultimately results in death (a natural paraphrase would be, “You will become mortal”), or (2) God mercifully gave man a reprieve, allowing him to live longer than he deserved.
Heb “dying you will die.” The imperfect verb form here has the nuance of the specific future because it is introduced with the temporal clause, “when you eat…you will die.” That certainty is underscored with the infinitive absolute, “you will surely die.” sn The Hebrew text (“dying you will die”) does not refer to two aspects of death (“dying spiritually, you will then die physically”). The construction simply emphasizes the certainty of death, however it is defined.The Hebrew text (“dying you will die”) does not refer to two aspects of death (“dying spiritually, you will then die physically”). The construction simply emphasizes the certainty of death, however it is defined. Death is essentially separation. To die physically means separation from the land of the living, but not extinction. To die spiritually means to be separated from God. Both occur with sin, although the physical alienation is more gradual than instant, and the spiritual is immediate, although the effects of it continue the separation.