John Calvin says (Commentarium in epistolam ad Hebraeos, translated by John Owen in 1853):
Were any one to object and say, that some had died twice, such as Lazarus, and not once; the answer would be this, - that the Apostle speaks here of the ordinary lot of men; but they are to be excepted from this condition, who shall by an instantaneous change put off corruption, (1 Corinthians 15:51;) for he includes none but those who wait for a long time in the dust for the redemption of their bodies.1
Therefore, he reads this text as referring to a general rule: the scope of the passage is not meant to speak about these various special cases. In particular, Calvin thinks the author is primarily addressing the normal case of people who die once and then stay dead for a long time. The cross-reference inserted by Owen is illuminating; Paul writes there:
Behold, I shew you a mystery; We shall not all sleep, but we shall all be changed. KJV
This chimes with other New Testament references to the living and the dead (traditionally, in English, "the quick and the dead") as in Acts 10:42, 2 Timothy 4:1, 1 Peter 4:5. In 1 Thessalonians 4:15-17, we read:
We which are alive and remain unto the coming of the Lord shall not prevent them which are asleep. For the Lord himself shall descend from heaven with a shout, with the voice of the archangel, and with the trump of God: and the dead in Christ shall rise first: then we which are alive and remain shall be caught up together with them in the clouds, to meet the Lord in the air: and so shall we ever be with the Lord. KJV
The fates of Elijah and Enoch are basically this, but earlier: they were taken up by God in the same way, albeit in anticipation of the coming of Christ, rather than after it. They have been seen as prototypes (in the sense of "characteristic or normative" rather than "rudimentary experiments") for the transformation Paul discusses in 1 Corinthians 15.
If we accept Calvin's scoping, then Elijah and Enoch are also explained. Lazarus is not a counterexample to the basic point of the author of Hebrews, and neither are they. In the same way, the judgement of those who are alive at the time of Jesus's return isn't a counterexample either. For one thing, everybody does eventually face a final judgement following the end of their earthly life, whether that period of their existence is terminated by normal death or by something else.
1. Si quis obiiciat, bis quosdam esse mortuos, ut Lazarum et similes: expedita est solutio, apostolum hic de ordinaria hominum conditione disputare, quin etiam ab hoc ordine eximuntur quos subita immutatio corruptione exuet: quia non comprehendit nisi eos qui diu in pulvere corporum suorum redemptionem exspectant.