What is the connection between the episode of Lemech, and the birth of Adam's third son?
Rashi: Lemech met Adam and complained to him about his wives, who were refusing to be intimate with him. 1 Adam rebuked them and told them that they should fulfill their obligations, and that Hashem's decrees were not their business. They retorted that he should practice what he preached, since for the last hundred and thirty years, he had not been intimate with his wife, from the time that he was given the death-sentence. Therefore the Torah continues "Va'Yeida Adam Od es Ishto". 2
Oznayim la'Torah (based on the Tanchuma): When Adam saw the disintegration of his son Kayin's descendents - when Lemech killed Kayin, the earth opened-up and swallowed Chanoch, Iyrad, Mechuyael and Mesushael - he realized that they were all destined to be destroyed, so he set about rebuilding.
Gur Aryeh: How does Rashi derive this? The Torah relates specifically now that Adam reunited with Chavah. Also, since this seems to be a new topic, why doesn't the Torah begin a new paragraph? It must be that the incident of Lemech's wives is what brought about Adam and Chavah having more children.
Why does the Torah add the word, "va'Yeida Adam Od"?
Rashi: To teach us that, despite one hundred and thirty years of abstention, his desire for his wife was stronger than before.
Here it says that 'she' called him Sheis. Below (Bereishis 5:3), it says that 'he' called him Sheis!
Chizkuni: Below it discusses the generations (it mentions only the men), so it is proper to attribute the name to Adam.
Malbim: Chavah thanked Hashem for giving a replacement son. Adam added a new intent - [Sheis] will be the foundation of the world. 1 The word "ha'Shasos" (Tehilim 11:3) means the foundations.
Adam had more children afterwards (Bereishis 5:4). Perhaps he knew through prophecy that in the future, all people will be from Sheis.
What is "Zera Acher"?
Moshav Zekenim: It is seed that is established elsewhere, i.e. Melech ha'Mashi'ach.
QUESTIONS ON RASHI
Rashi writes: "'va'Yeida Adam Od;' what is meant by 'Od' (more)?" Why not interpret it simply to mean [that he was intimate with Chavah] an additional time?
Gur Aryeh: The word "Od" (more) usually means adding onto something that is still extant. For example "She conceived again (va'Tahar Od)" (29:33) means another pregnancy in addition to the first baby who had already been born. Sometimes, "Od" means immediate repetition of an action. Here, the Pasuk says "va'Yeida Od," and neither is the case; the first instance of intimacy had ceased long before this one. Therefore, Rashi explains that the intimacy was qualitatively more.
Rashi writes: "The word 'Od' teaches you that [Adam's] previous desire was enhanced with even more desire." What does this come to teach us?
Gur Aryeh: According to the Midrashim, this means that Adam desired Chavah even when he did not see her. The additional desire shows how Hashem wanted them to conceive at that time, for the world would continue from that child. 1
Gur Aryeh: We find a parallel for this in the Midrash regarding Yehudah and Tamar (Bereishis 38:16). Also refer to 5:3:0.1:1.
