I think that “il” actually replaces the infinitive subordinate clause:

*”Nous ramener quelque chose lui arrive” is the idea behind the sentence.

Your sentence is just fine.

Here in “il lui arrive” il does not refer to fille, it’s the subject
of impersonal use of verb arriver (il arrive que), like in “il faut que”,
“il se trouve que…” etc.

Here is a sentence using a similar structure.

Après s’être préparée, un vilain coup de vent lui retarda son projet de navigation de plusieurs heures.

The active subject of the first clause was her, whoever she is. She appears again as “lui”, substituted for “elle”, in the second clause, as the victim of a “vilain coup de vent” that delays her departure.

The sequence of events is clear (AFTER she got ready came an event that prevented her from departing immediately).

The status of the different actors and the relation between the consequences of their actions is also clear (BECAUSE the wind got worse than it was, she had to postpone her travel, though she was otherwise ready to go).

Everything is so clear that it would be hard to call it ungrammatical. Of course we could reorganize the sentence, but it is neither necessary nor would it make it a lot less ambiguous.

Here is another such sentence where the subject of the first clause (JE) is not even present in the second clause. However, it does remain clear, and it is from the highest authority of the French language.

Je n’irai point là QUE tout ne soit prêt. –Dictionnaire de l’Académie, 4e édition

In this case again, the meaning is clear: JE will not be found THERE prior to “everything being ready”.

Here are other examples from worthy authors:

Une heure après qu’Albertine était couchée, j’allai jusqu’à son lit. –Marcel PROUST, À la recherche du temps perdu

La pluie avait cessé que nous allions encore à toute vitesse –Georges DUHAMEL, Les hommes abandonnés

Back to the original sentence in the question:

Ta fille est partie jouer. Après s’être amusée, il lui arrive de nous ramener quelque chose d’intéressant.

The sequence of events is clear (AFTER she’s done playing, SHE sometimes bring something interesting back).

SHE is also present in the second clause, though as a secondary actor, and as the perhaps unintuitive LUI.

So the main subject of the first clause is still less of an abstraction in the second clause than it is in the Academy example.

The sentence could also easily be reorganized, though it would add very little clarity to this already correctly formed statement:

Après s’être amusée, ELLE nous ramène parfois quelque chose d’intéressant.

Conclusion: the sentence is correct. Not very many people will complain about it, because it is clear, similar examples are attested by good writers and by the Academy, and it achieves its main intent of communicating what it has to communicate.