The Idea in Brief
The context appears to include both: that is, life despite ("even though") death and life after death. The statement also implies the obverse: those who are alive but do not believe are dead.
Discussion
The passage occurs as follows in the 28th Revised Edition of Aland's Greek New Testament (2012).
John 11:25 (mGNT)
25 εἶπεν αὐτῇ ὁ Ἰησοῦς· ἐγώ εἰμι ἡ ἀνάστασις καὶ ἡ ζωή· ὁ πιστεύων εἰς ἐμὲ κἂν ἀποθάνῃ ζήσεται,
The phase καὶ ἡ ζωή occurs in variant other minuscules and manuscripts, but the editors of the 28th Revised Edition ("the Committee") ascribed their highest confidence {A} that these words were the authorial intent. Metzger (1994) writes that
καὶ ἡ ζωή {A}
The omission of καὶ ἡ ζωή from several witnesses (P45 it1 syrs palms, Diatessaronsyr Cyprian Paulinus-Nola) is puzzling. Was it added in the great mass of witnesses in anticipation of the thought expressed by the following ζήσεται and ὁ ζῶν, or was it omitted, perhaps by accident in transcription or because ver. 24 makes mention of the resurrection alone? On the basis of considerations of the age, weight, and diversification of witnesses that include the words, a majority of the Committee preferred to retain them in the text.
The following translation from the NASB thus provides the accurate rendering of this verse in context:
John 11:25-26
25 Jesus said to her, “I am the resurrection and the life; he who believes in Me will live even if he dies (ἀποθάνῃ), 26 and everyone who lives and believes in Me will never die (ἀποθάνῃ). Do you believe this?”
In the context, Jesus is juxtaposing the verb ἀποθάνῃ with two distinct nuances. In the first mention in v.25, the dying is visible (physical), and in the second mention in v.26, the dying is invisible (spiritual). In the latter case, Jesus qualifies the subjunctive verb with οὐ μή, for which Smyth (1920) explains is translated in the future tense, indicative mood.
οὐ μή
2754 . οὐ μή, and the compounds of each, are used in emphatic negative predictions and prohibitions.
a. οὐ μή marks strong personal interest on the part of the speaker. In its original use it may have belonged to colloquial speech and as such we find it in comedy; but in tragedy it is often used in stately language. οὐ μή is rare in the orators.
2756 . (II) In strong prohibitions (cp. 1919).
a. With the future indicative (second person singular). Thus, οὐ μὴ καταβήσει don’t come down Ar. Vesp. 397.
b. With the aorist subjunctive rarely (1800 N.). Thus οὐ μὴ ληρήσῃς don’t talk twaddle Ar. Nub. 367. Many editors change the aorist subjunctive to the future indicative. (Emphasis added)
In other words, if the believer in Jesus dies (physical sense) they will live after death, because they can never die (spiritual sense). Jesus demonstrated his power of life through his command to raise Lazarus from the dead.
On the other hand, for those who do not believe in the Son, they "live" or exist in a state of perpetual spiritual death.
John 3:36 (NASB)
He who believes in the Son has eternal life; but he who does not obey the Son will not see life, but the wrath of God abides on him.
Thus the statements of Jesus (which include the verse immediately, above) state that those who are "alive" -- but do not believe -- are dead both now and forever. That is, they will remain in a state of perpetual spiritual death if they do not receive eternal life, which is the invisible baptism that "washes away" their spiritual death (the living water).
Conclusion
Jesus provides eternal life ("living water" in John 4:14) to those who believe in him. This eternal life is received today, and will continue after death. The Apostle John affirms as follows:
1 John 5:13 (NASB)
These things I have written to you who believe in the name of the Son of God, so that you may know that you have eternal life.
In summary, in the context of these writings by the Apostle John, the believer will receive eternal life in the present time despite ("even though") physical death may occur at some point; however, this eternal life will also continue after death. In this latter sense, the believer will never die.
REFERENCES:
Aland, K., Aland, B., Karavidopoulos, J., Martini, C. M., & Metzger, B. M. (2012). Novum Testamentum Graece (28th Edition., Jn 11:25). Stuttgart: Deutsche Bibelgesellschaft.
Metzger, B. M., United Bible Societies (1994). A textual commentary on the Greek New Testament, second edition a companion volume to the United Bible Societies’ Greek New Testament (4th rev. ed.) (p. 199). London; New York: United Bible Societies.
Smyth, H. W. (1920). A Greek Grammar for Colleges. New York; Cincinnati; Chicago; Boston; Atlanta: American Book Company, 626-627.
