Une seule de ces vies a un avenir. L’autre n’en a aucun.

As Laure and jlliagre note already in the comments en refers to avenir. It is used here as a personal pronoun so that to avoid repeating avenir.

Une seule de ces vies a un avenir. L’autre (i.e. de ces vies) n’a aucun avenir.

Une seule de ces vies a un avenir. L’autre (i.e de ces vies) n’a pas d’avenir.

En Replaces a THING Introduced by a Verb Followed by “de, du, de la, de l’, des”.

Je rêve de mes vacances = j’en rêve

Je parle de mon avenir = j’en parle

See for instance here:

https://www.frenchtoday.com/blog/french-grammar/how-to-use-the-pronoun-en-in-french/

https://www.carleton.edu/french/resources/language-tools/grammar/object_pronouns/#y

The use of the “en” pronoun

Should we wish an explicit de, following @jlliagre (thanks!), here it is:

D’avenir, elle n’en a pas.

EDIT

There is no need for an explicit de in fact.

Il y a quelques personnes, beaucoup, peu de personnes, un peu, trop,
assez de monde… -> Il y en a quelques-unes, beaucoup, peu, un peu,
trop, assez…

Il n’y a aucune personne. Il n’y en aucune.

It does not make sense but asking yourself:

L’autre (de ces vies) a-t-elle beaucoup d’avenirs?

Elle (l’autre de ces vies) n’en a aucun.

See: http://w3.restena.lu/amifra/exos/gram/regprpers.htm

The rule you know is not complete; here is a rule that is probably complete; anyway it takes the case you mention into account; it is found in this site;

Le pronom « en » remplace

• un nom introduit par « de » (où « de » est la préposition)¹
• un nom introduit par un article partitif ou un article indéfini (un, une, de, des)²
• Pour les personnes, on utilise les pronoms toniques et non le pronom en.
  Ex : Vous parlez du patron ? Oui, nous parlons de lui.

The indefinite article referred to in your sentence is « un ».

¹_{Addition by user LPH}
²_{Addition of the 4 articles by user LPH}

COMPLEMENT (prompted by user Alan Evangelista and without support as this explanation of mine is all I could find to clarify this matter)

It is not as perfect as you think; the scheme of representation by pronouns is ideal for personal pronouns as far as persons go; as soon as you start using “it” you run into problems looking for the right form: (ex.: — He said he was bold. — It is not something I’d say of myself._ What is “It”? ). The same is true in French.

In the first part of the rule the representation is faithfull;

• Vous avez envie de chocolat ? Oui, nous en/de chocolat avons envie !

It is also faithfull in the case of partitives as long as a term for a specifying quantity is not added;

Il y a du lait ? Oui il y en/du lait a.

or Oui, il y en a 2 litres.

In this case you can say instead “Oui, il y a deux litres de lait.”. You remark then that “du lait deux litres” is not the required syntax; what’s needed is “deux litres de lait”. The scheme of perfect representation is at its end.

It is not perfect any more when an indefinite article; notice that the rule in the link that provides it says that in this case “Il est important d’ajouter une expression de quantité quand on veut donner plus de précisions”; we’ll see now that in some cases of indefinite article it is not only important, it is compulsory.

• Est-ce que tu as acheté une poêle hier ?

• Oui, j’en ai acheté.

  that’s not correct, you have to add a specification of quantity.

• Oui, j’en ai acheté une.

• Oui, j’en ai acheté trois pour être sûr d’avoir celle qu’il faut.

“En” stands for “poêle” then and not “une poêle”. In fact “en” communicates the generic idea of the thing in question : Oui, je parmi les choses appelées « poêle » ai acheté une.

In the case you study “aucun” is that necessary specification of quantity, here it is simply zero. You couldn’t, as in the example I chose say “Il n’en a.”; that would have no meaning at all; this difference is due to the use of an indefinite article.

It is important to understand that this is subject to the sort of indefinite article you consider;

• Est-ce que tu as acheté des pommes hier ?
• Oui, j’en ai acheté. Oui, je en/*parmi ces articles appelé “poêles” ai acheté.

That is correct, you do not have to add a specification of quantity.

Here you might believe that a true representation is again the norm but it is not so; the generic scheme is what prevails. The absence of the quantity specification is due apparently to an anomaly; there is no pronoun “des” corresponding to the indefinite article “des” as there is a pronoun “un” corresponding to indefinite article “un”

• Oui, mais je n’en ai acheté qu’une.
• Oui, j’en ai acheté trois pour être sûr d’avoir celle qu’il faut.

 

• Il y pêchait de grands poissons à la chair tendre. (indefinite article “de”)

• Oui, c’est vrai, il en pêchait souvent.
  No necessity for a specification of quantity again but it remains a possibility

• Oui, il en pêchait (beaucoup/dix par jour/un de temps en temps…).

You now hit upon a subtle point when you ask yourself what is the relation with “le”; why not use “le” ? The very reason is exactly contained in what I’ve tried to make clear to you; it’s because you do not need any more a generic reference to the thing in question as you are talking about the particular specimen mentioned first. In other words “le” refers to that particular “avenir” or said differently, represents it, whereas “en” refers to that thing generically, as a sort, and thus it represent that sort, that sort out of which you select one or any number of elements or even zero.

“en” does not always replace “de quelque chose”.

To pronominalize an object used with an indefinite article, you need both “en” and “un(e)”.

• J’ai un avenir. → J’en ai un.
• Je n’ai pas d’avenir. → Je n’en ai pas.
• Je n’ai aucun avenir. → Je n’en ai aucun.