When expressing that an item is part of a collection, you can write either un(e) de or l'un(e) de. The meaning is the same in this sentence (there might be a slight nuance sometimes). In particular, using l'un does not bring any sense of primacy.
I can't find a general rule as to when the extra article is used. In some constructions it cannot be used, in others it feels weird to omit it. The Trésor de la langue française (you want un³, the pronoun) gives some idea of the usage frequency in various contexts.
Including l' makes the example more specific, so it cannot be used when the example is one of many interchangeable items. For example (Mérimée, cited in TLF): « nous passions dans une de ces ruelles étroites comme il y en a tant à Séville » — the narrator probably wouldn't be able to find the street again, so the definite article cannot be used.
I think the article is compulsory when the collection is a pronoun, probably for euphonic reasons : l'un d'eux, l'une d'elles (or l'un d'entre eux, l'une d'entre elles — entre is added to avoid an overly long sequence of words that look like pronouns, it can be used in other cases but then tends to feel cumbersome).
The article is also compulsory in l'un(e) ou l'autre (“one or the other”).
In the general case, such as your example sentence, l' is permissible but can be omitted. It is more common to include it in formal writing. There is no difference in meaning.