The Garden of Eden Story is very complex and it seems to me that both the Serpent and God fall short of telling the absolute truth.
טז וַיְצַו יְהוָה אֱלֹהִים, עַל-הָאָדָם לֵאמֹר: מִכֹּל עֵץ-הַגָּן, אָכֹל תֹּאכֵל. 16
And the LORD God commanded the man, saying: 'Of every tree of the garden thou mayest freely eat;
יז וּמֵעֵץ, הַדַּעַת טוֹב וָרָע--לֹא תֹאכַל, מִמֶּנּוּ: כִּי, בְּיוֹם אֲכָלְךָ מִמֶּנּוּ--מוֹת תָּמוּת. 17
but of the tree of the knowledge of good and evil, thou shalt not eat of it; for in the day that thou eatest thereof thou shalt surely die.'
God tells man that on the day he eats of the tree he will surely die. We know later on that he lives for almost a thousand years. Eve seems to be reading the verse the way I'm describing as she is even afraid to touch the tree for fear of death.
ב וַתֹּאמֶר הָאִשָּׁה, אֶל-הַנָּחָשׁ: מִפְּרִי עֵץ-הַגָּן, נֹאכֵל.
2 And the woman said unto the serpent: 'Of the fruit of the trees of the garden we may eat;
ג וּמִפְּרִי הָעֵץ, אֲשֶׁר בְּתוֹךְ-הַגָּן--אָמַר אֱלֹהִים לֹא תֹאכְלוּ מִמֶּנּוּ, וְלֹא תִגְּעוּ בּוֹ: פֶּן-תְּמֻתוּן.
3 but of the fruit of the tree which is in the midst of the garden, God hath said: Ye shall not eat of it, neither shall ye touch it, lest ye die.'
The Serpent seems to be hinting that the fruit won't kill her in the way that she thinks, and adds another reason why God wouldn't want her or Adam to eat from the tree.
ד וַיֹּאמֶר הַנָּחָשׁ, אֶל-הָאִשָּׁה: לֹא-מוֹת, תְּמֻתוּן.
4 And the serpent said unto the woman: 'Ye shall not surely die;
ה כִּי, יֹדֵעַ אֱלֹהִים, כִּי בְּיוֹם אֲכָלְכֶם מִמֶּנּוּ, וְנִפְקְחוּ עֵינֵיכֶם; וִהְיִיתֶם, כֵּאלֹהִים, יֹדְעֵי, טוֹב וָרָע.
5 for God doth know that in the day ye eat thereof, then your eyes shall be opened, and ye shall be as God, knowing good and evil.'
The Serprent brings a new concept to the table, the idea that God might actually be afraid of Adam and Eve if they eat of the tree. The Serpent's words end up being true as the story ends with God seeming to be afraid of Adam and Eve for the exact reason that the serpent gave, that Adam and Eve had become like God. God never spoke of this being an issue to Adam and Eve, and yet it's the sole reason God speaks of when He evicts Adam and Eve from the garden.
כב וַיֹּאמֶר יְהוָה אֱלֹהִים, הֵן הָאָדָם הָיָה כְּאַחַד מִמֶּנּוּ, לָדַעַת, טוֹב וָרָע; וְעַתָּה פֶּן-יִשְׁלַח יָדוֹ, וְלָקַח גַּם מֵעֵץ הַחַיִּים, וְאָכַל, וָחַי לְעֹלָם.
22 And the LORD God said: 'Behold, the man is become as one of us, to know good and evil; and now, lest he put forth his hand, and take also of the tree of life, and eat, and live for ever.'
כג וַיְשַׁלְּחֵהוּ יְהוָה אֱלֹהִים, מִגַּן-עֵדֶן--לַעֲבֹד, אֶת-הָאֲדָמָה, אֲשֶׁר לֻקַּח, מִשָּׁם.
23 Therefore the LORD God sent him forth from the garden of Eden, to till the ground from whence he was taken.
And before anyone here tries to say that Adam and Eve died later and so God wasn't lying, you need to give proof of this. Because if Adam and Eve were already immortal before being commanded not to eat of the forbidden fruit, then what good is the tree of life? And if they are destined to die according to God from eating the forbidden fruit, then how could the tree of life save them/grant them immortality?