There is no harm in a lame animal if it can walk to the place of sacrifice

It is narrated from Hujayyah bin Adi that a man asked Sayyiduna Ali (may Allah be pleased with him) about a cow, and he said: It is (sufficient) on behalf of seven people. He asked: What if its horn is (broken)? He said: That will not harm you. He asked: What if it is lame? He said: If it reaches the place of slaughter by walking (then it is permissible). And he further said that the Messenger of Allah (peace and blessings be upon him) had commanded us to examine the eye and the ear (of the sacrificial animal) carefully.

It is narrated from Hujayyah bin Adi that a man asked Sayyiduna Ali (may Allah be pleased with him) about sacrificing a cow, and he said: It is on behalf of seven people. He asked: What if its horn is broken? He said: There is no harm. He asked: What if it is lame? He said: If it reaches the place of sacrifice. And he said: The Messenger of Allah (peace and blessings be upon him) commanded us to examine the eye and the ear carefully.

Hujayyah bin Adi said: I heard Sayyiduna Ali (may Allah be pleased with him) when a man asked him about a cow, and he said: It is on behalf of seven people. He asked him about the horn, and he said: That makes no difference. He asked him about lameness, and he said: If it reaches the place of slaughter (that is, if it can walk on its own feet to the place of sacrifice). And the Messenger of Allah (peace and blessings be upon him) commanded us to examine the eye and the ear carefully.
All of these chains are sahih (authentic). Although the two Shaykhs did not use Hujayyah bin Adi as evidence, he is among the senior companions of the Commander of the Believers, Ali (may Allah be pleased with him).

It is narrated from Yazid bin Khalid al-Misri; he said: I came to Sayyiduna Utbah bin Abd al-Sulami (may Allah be pleased with him) and said: O Abu al-Walid! I went out looking for sacrificial animals, but I did not find anything that pleased me except a tharma' (one whose front teeth have fallen out), and I disliked it. What is your opinion? He said: Why did you not bring it to me? I said: Subhan Allah! Is it valid on your behalf and not valid on mine? He said: Yes, because you are in doubt and I am not in doubt. The Messenger of Allah (peace and blessings be upon him) only forbade (sacrificing) these animals: the musfarrah (one whose ear has been cut off from the root until its ear-hole becomes visible), the musta'salah (one whose horn has been broken off from the root), the bakhqa' (one whose eye has been put out), the mushayya'ah (one that lags behind the flock because it is emaciated and weak), and the kasra' (a lame animal with broken limbs).
This hadith has an authentic chain (sahih al-isnad), but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Sayyiduna Ibn Abbas (may Allah be pleased with them both) that the Messenger of Allah (peace and blessings be upon him) said: "Among the large sacrificial animals (camels and the like), these are not permissible: the one-eyed animal, the emaciated animal, the mangy animal, and the animal whose teats have been cut off (from the root)."
This hadith has an authentic chain (sahih al-isnad), but the two Shaykhs (Bukhari and Muslim) did not record it.