It writes here the following:
May one read stories of Tzaddikim in a bathroom?1
Stories from Tanach and the Talmud are forbidden to be read in a bathroom as they are actual words of Torah. However stories of other Tzaddikim and Gedolei Yisrael seemingly may be read in a bathroom.2
1Piskeiy Teshuvos 85/3; Vayivarech David 15
2 ibid; To note that the sons of the Alter Rebbe read him stories of Tzaddikim while he was receiving medical treatment in the bathtub, seemingly in order to prevent him from thinking words of Torah. However when they came to talk of the Tzaddik Rav Shmelka of Nikulsberg Admur stated that of such a holy Tzaddik they cannot talk about in a bathroom. [Shmuoes Usipurim Vol. 1 p. 241]
If the content of the book contains Torah or shiurim of the said Gadol. Rav Moshe Shternbach shlita in Teshuvos V'hanhagos, cheilek beis, siman 466 brings a case that is perhaps transferable, namely the topic of frum newspapers that contain divrei Torah and whether one can enter into the bathroom with them.
It writes here:
When there is a newspaper which mentions, by the way, these Torah like ideas, where it is clear that one's intent is to read the story, and not to learn the words of Torah, it is permitted to take them into the bathroom. If though the name of G-d is written out fully, then it is forbidden.
However it is worth noting that he states:
ולכן לע"ד יש יסוד למקילין להכניס עתונים לבית הכסא, אכן להכניס לשם מאמר מיוחד לדברי תורה זהו בזיא מלתא ואסור מעיקר הדין אלא יקרענו מהעתון ולא יכנס עמו
And therefore according to my humble opinion, there is a basis to be lenient to enter into the bathroom with such newspapers. However, if there is a special article that contains divrei Torah then it is disgrace (to enter it into the bathroom) and it is forbidden from the fundamental din (law) and rather one should tear it out from the newspaper and not bring it (into the bathroom) with him.
So it would seem from Rav Shternbach shlita that one could bring in the book if it only has Torah-like expressions but one should avoid bringing it in if it contains divrei Torah and the like.