Most tafsir books expand on explaining the meaning of pairs or mates in the verse (11-40) and hardly offer any explanation on the kinds of animals that have been taken on the ark.
... We said, "Load upon the ship of each [creature] two mates and your family, except those about whom the word has preceded, and [include] whoever has believed." But none had believed with him, except a few. (11:40)
So the few information on which kind of animals have been taken on the ark basically seems to be less reliable. The fact that the scholars quoting them however use the Arabic form of passive voice emphasize some doubts on the authenticity and reliability of the narrations:
At this point, Allah commanded Nuh to select one pair from every kind of creature possessing a soul, and load them on the ship. Some said that this included other creatures as well, such as pairs of plants, male and female. It has also been said that the first of the birds to enter the ship was the parrot, and the last of the animals to enter was the donkey. (source qtafsir)
qtafsir here didn't quote the rest of the story saying that a-Shaitan has entered the ark suspended at the donkey tail ... which is the continuation of the quote in tafsir ibn Kathir.
Further ibn Kathir offers a solution for the lion:
وذكر أبو عبيدة بن عبد الله بن مسعود أنهم لم يستطيعوا أن يحملوا معهم الأسد ، حتى ألقيت عليه الحمى (source: tafsir ibn Kathir)
My translation take it carefully:
It was mentioned -passive voice- by abu 'Obayda ibn 'Abdullah ibn Mas'ud that they couldn't take the lion until, he became or was befallen with fever (by Allah).
Al-Baghawy quoted it entiteling it as a story (or tale):
وفي القصة : أن نوحا عليه الصلاة والسلام قال : يا رب كيف أحمل من كل زوجين اثنين؟ فحشر الله إليه السباع والطير ، فجعل يضرب بيده في كل جنس فيقع الذكر في يده اليمنى والأنثى في يده اليسرى ، فيحملها في السفينة . (source tafsir al-Baghawy)
My own translation take it carefully (note that I'm unsure about the correct translation of the bold words):
In the story: it was said that Nuh peace and Blessings be upon him said: Oh my Lord how can I care two mates? Allah sent to him lions (more exactly beast animals) and birds, so he started reaching out for each kind, so that the males fell in his right hand while the females fell in his left hand, then he carried them to the ark (ship).
Al-Baghawy also quoted the story of Satan and the donkey on the authority of ibn 'Abbas and a story of the serpent and the scorpion who first were refused to enter the ark.
Ibn abi Hatim quoted several narrations on his own authorithy in his tafsir, I'll try to quote and translate them in my own words -take it carefully- I've eliminated the narrator chain just to shorten the quotes:
لما أمر نوح عليه السلام أن يحمل معه في السفينة من كل زوجين اثنين لم يستطع يحمل معه الأسد حتى ألقيت عليه الحمى فحمله فأدخله.
 from abu 'Obaydah who said:
when Nuh peace be upon him was ordered to load two mates, he was not able to load the lion until the fever has befallen him then he toke and got him inside.
 لَمَّا حَمَلَ نُوحٌ الْأَسَدَ فِي السَّفِينَةِ اشْتَهَى اللَّحْمَ فَزَادَ مَخَافَةَ أَهْلِ السَّفِينَةِ، فَشَكَوْا ذَلِكَ إِلَى نُوحٍ، فَدَعَا عَلَيْهِ، فَأُلْقِيَتْ عَلَيْهِ الْحُمَّى فَمَرَّ بِهِ نُوحٌ.
from Mubarak who said I heard Bakr saying:
when Nuh had loaded the lion in his ark (ship) he desired flesh, the people inside the ark became more frightened and complained to Nuh the he made a supplication and the lion became fever, Nuh then passed by him.
 " لَمَّا حَمَلَ نُوحٌ فِي السَّفِينَةِ مِنْ كُلٍّ زَوْجَيْنِ اثْنَيْنِ، قَالَ أَصْحَابُهُ: وَكَيْفَ نَطْمَئِنُّ أَوْ تَطْمَئِنُّ الْمَوَاشِي، وَمَعَنَا الْأَسَدُ فَسَلَّطَ اللَّهُ عَلَيْهِ الْحُمَّى، فَكَانَتْ أَوَّلَ حُمَّى نَزَلَتْ فِي الْأَرْضِ ثُمَّ شَكَوُا الْفَأْرَةَ, فَقَالُوا: الْفُوَيْسِقَةُ تُفْسِدُ عَلَيْنَا طَعَامَنَا وَمَتَاعَنَا، فَأَوْحَى اللَّهُ إِلَى الْأَسَدِ فَعَطَسَ، فَخَرَجَتِ الْهِرَّةُ، فَتَخَبَّأَتِ الْفَأْرَةُ مِنْهَا".
From Zaid ibn Aslam from his father who said that the Messenger of Allah peace and Allahs blessings be upon him said:
when Nuh loaded in his ark (ship) from each kind two mates, his companions said: How can we be secure or our cattle while the lion is with us. Then Allah sent fever to the Lion, and this was the first fever on earth, then they complained about the mouse, and they complained: the mouse makes our food corrupt and destroys our belongings. Allah then made the lion sneeze and a cat came to life, Then the mouse hide herself from it.
This last narration has the most connected narrator chain (of known narrators, most are trustworthy) from the father of the author until the prophet () which may define this report as a hadith.
Conclusion: According the collected narrations, one could say the mainline is that either Allah () directly or as a response to the supplication of Nuh () made the lion suffer from a fever to make him calm and harmless during his stay on the ark. Other narrations also quote the presence of Elephants.