For instance, Midrash Eichah is on the list in the Mechaber (OC 554:2). One piece in there discusses the comparison between the Eichah's mentioned by Moshe, Yeshaya, and Yirmiya (Eichah Rabbah 1:1). Let's say I want to understand the Midrash a little better, so I want to look at those three passages inside. Obviously the one said by Yirmiya - Megillas Eichah - is okay, but are there any leniencies to permit reading the passage in Devarim 1 and Yeshaya 1, where those Eichah's are mentioned, in order to better understand the text at hand?
In Kitzur Shulchan Aruch 124:5 it's written (emphasis mine):
דברי תורה משמחין את הלב, שנאמר פקודי ה' ישרים משמחי לב. ולכן אסור בתשעה באב ללמד תורה, כי אם בדברים שמעציבים את לבו, כגון בספר ירמיה בדברים הרעים שבו, ופסוקי נחמה שבו ידלג. וכן פרעניות על אמות העולם שכתובות שם ידלג. וכן מתר ללמד בספר איוב, ומדרש איכה, וגמרא פרק אלו מגלחין וכו, דמירי בדיני אבל ומנדה, ובהגדה דפרק הנזקין, וירושלמי סוף מסכת תענית, דמירי מחרבן. ואף באלו שהוא מתר ללמד, אסור לעין בהם איזה קשיא ותרוץ או דרוש, כי משמחים את הלב. וכל מה שמתר האדם ללמד בעצמו, מתר ללמד גם עם תינוקות. מתר לקרות כל סדר היום, אפלו איזהו מקומן. וסדר מעמדות אין לומר, אפלו מי שרגיל לאמרו בכל יום - תקנד
The words of Torah make the heart glad as it is said: ''The statutes of the Lord are right, rejoicing the heart'', therefore it is forbidden on the 9th of Av to learn Torah, excepting those topics which sadden one's heart, for example in the book of Jeremiah the evil (prophecies) in it, and the verses of comfort should be omitted. Also the calamities on the nations of the world that are written there are omitted. It is allowed to study the book of Job, and the midrash on Lamentations, and the Gemara ''And these can shave on the festival...'', which covers the laws of mourning and ostracism, and the stories (of the destruction of Jerusalem and Beitar) in (Gittin) the (fifth) chapter ''Damages'', and the Jerusalem Talmud at the end of tractateTa'anit (Fast) which covers the destruction of the Temple. However, even in these that one is allowed to study, it is forbidden to enter in to any (halachic) difficulty, or explanation or commentary, because (these) bring pleasure to the heart. Everything that one is allowed to learn by oneself, one can also teach to children. One can read (all the Torah topics in) the daily order of prayer even ''Which were the places...''. The order of ''Ma-amodot'' are not said even by one who is accustomed to saying it every day.
The implication from here (and DoubleAA was hinting to it in his comment) is that the purpose of being allowed to learn only specific areas of Torah is to cause one to become more emotionally involved in the day. Getting too caught up in the details of the piece of Torah being learnt changes the exercise from being an emotional one to a logical one, which seemingly wouldn't be allowed according to the Kitzur.
However, last Shabbos, during the weekly Gemara Taanis Shiur given by one of local Rabbonim in my community, we were discussing the source for this in the Gemara (Daf 30a), and the Rav mentioned the opinion of the Chazon Ish who holds differently than the Kitzur. While I don't have the source, the gist of what was quoted from the Chazon Ish was that it's not possible for one to truly 'learn' something without delving deeply into the subject, and if the Chachomim allowed one to learn specific topics, then one must be allowed to delve as deeply into the subject as one can.
Therefore, it would seem like based on this second opinion, you would be allowed to follow the chain of sources in order to better understand the piece that you are learning.