Your sentence is wrong.

C’est la première fois que je visite le musée, le cinéma, etc.

That is, visiter quelque chose.

C’est la première fois que je rends visite à Georges (man)/Hélène (woman)/. => C’est la première fois que je lui rends visite (and not visiter !!!).

That is rendre visite à quelqu’un.

[Google Translate actually gives the correct translation.]

Man or woman is immaterial, inasmuch as the expression is rendre visite à quelqu’un (googling complément d’objet indirect or French Dative).

For a group of people (immaterial of sex) it would be:

C’est la première fois que je leur rends visite.

One should learn “rendre visite à” as a fixed expression (expression figée). There is no reason to break it into different parts. In expressions of this kind one should not isolate, for instance, rendre from visite and so on.

In compound tenses there is no need of agreement of the past participle. That is, one would say in passé composé

C’est la première fois que je lui ai rendu/leur ai rendu visite.

This is the basic usage; sufficient for débutants/faux débutants of the French language. For more details see here:

« Visiter » vs « rendre visite à » ?.

As @jlliagre clarifies:

You write “This is the first time I visit her (a girl). That’s why lui is needed”. In fact, should lui has been needed, that would actually be le at the masculine (c’est la première fois que je le visite) and elle at the feminine (c’est la première fois que je la visite). Still incorrect though, as je lui rends visite is the right expression.

Also

C’est la première fois que je la visite is grammatically correct but if said by a native French speaker referring to a girl, will likely be understood as a joke or (possibly) with a sexual connotation.

and

In any case, we do not use that much the verb visiter here. The translation that first comes to mind is C’est la première fois que je vais (la voir) chez elle.

According to the book Larousse Thématique : Dictionnaire des difficultés de la langue française

(…) visiter peut se dire aussi pour “rendre visite”.

In particular the following examples are given (taken by Littré, Académie, Larousse du XXe siècle).

Visiter ses chefs. Visiter un ami. Visiter un malade.

Still from the same book

il (i.e. visite) se dit surtout pour les malades, les pauvres, etc.