Is there anything to prove that the punishment in Hell will be reduced for Abu Lahab?
Question

Are there any reports, saheeh or da‘eef (sound or weak) to suggest that the punishment in Hell would be reduced for Abu Lahab?
Praise be to Allah.Some verses in the Qur’aan indicate that the punishment for disbelief will not be reduced for the disbeliever under any circumstances. Allah says (interpretation of the meaning):
“But those who disbelieve, (in the Oneness of Allah - Islamic Monotheism) for them will be the Fire of Hell. Neither it will have a complete killing effect on them so that they die, nor shall its torment be lightened for them”
[Faatir 35:36]
“And those in the Fire will say to the keepers (angels) of Hell: ‘Call upon your Lord to lighten for us the torment for a day!’
They will say: ‘Did there not come to you, your Messengers with (clear) evidences and signs?’ They will say: ‘Yes.’ They will reply: ‘Then call (as you like)! And the invocation of the disbelievers is nothing but in error!’”
[Ghaafir 40:49-50]. 
With regard to the righteous deeds of the disbelievers, they will be rewarded for them in this world, with provision, children, and other blessings. They are people whose good things are hastened for them in the life of this world. But when it comes to the Hereafter, no rewards are decreed for them, because disbelief nullifies all good deeds and the good deeds of one who disbelieved are to no avail. However the disbelievers will vary in punishment in Hell, according to their crimes in this world, although they will all abide in Hell for ever and ever. Allah, may He be exalted, says (interpretation of the meaning):
“And We shall turn to whatever deeds they (disbelievers, polytheists, sinners, etc.) did, and We shall make such deeds as scattered floating particles of dust”
[al-Furqaan 25:23]. 
It was narrated that ‘Aa’ishah (may Allah be pleased with her) said:
I said: O Messenger of Allaah, during the Jaahiliyyah Ibn Jud’aan used to uphold the ties of kinship and feed the poor. Will that benefit him at all? He said: “It will not benefit him, because he did not say one day, ‘Lord forgive me my sins on the Day of Judgement.’”
Narrated by Muslim, no. 214 
Secondly: 
With regard to what was narrated about the punishment being reduced for Abu Lahab because he manumitted Thuwaybah, the wet-nurse of the Prophet (blessings and peace of Allah be upon him), this was not narrated from the Prophet (blessings and peace of Allah be upon him) or from the Sahaabah (may Allah be pleased with them). Rather it was a dream that was seen by some people, and it is not permissible to use it to contradict what was previously affirmed about the good deeds that the disbelievers do in this world not availing them anything before Allah, let alone the fact that this report is only narrated through a mursal isnaad (that is, the chain of transmission attributing it to the Prophet (blessings and peace of Allah be upon him) is incomplete). 
Al-Bukhaari (5101) narrated the following from ‘Urwah ibn az-Zubayr (may Allah have mercy on him): 
Thuwaybah the freed slave woman of Abu Lahab: Abu Lahab manumitted her and she breastfed the Prophet (blessings and peace of Allah be upon him). When Abu Lahab died, one of his family saw him (in a dream) in bad shape. He said to him: What happened to you? Abu Lahab said: Nothing happened to me after I left you except that I was given to drink of this for manumitting Thuwaybah. 
Ibn Hajar (may Allah have mercy on him) said: 
“Thuwaybah the freed slave woman of Abu Lahab” – she was mentioned by Ibn Mandah in as-Sahaabah. He said: There was a difference of opinion as to whether she became Muslim. Abu Nu‘aym said: We do not know of anyone who stated that she became Muslim except him. What it says in the books of Seerah (Prophet’s biography) is that the Prophet (blessings and peace of Allah be upon him) used to honour her and she used to enter upon him after he married Khadeejah, and he used to send gifts to her from Madinah. And after the conquest of Khaybar she died, as did her son Masrooh. 
“Abu Lahab manumitted her and she breastfed the Prophet (blessings and peace of Allah be upon him)” – the apparent meaning is that he manumitted her before she breastfed the Prophet (blessings and peace of Allah be upon him), but what appears in the books of Seerah is the opposite, which is that Abu Lahab manumitted her before the Hijrah (Prophet’s migration to Madinah), which was a long time after she had breastfed him. as-Suhayli also narrated that her manumission came before she breastfed the Prophet (blessings and peace of Allah be upon him). We shall quote his words below. 
“one of his family” – as-Suhayli stated that al-‘Abbaas said: When Abu Lahab died, I saw him in my dream one year later, in bad shape. He said: I found no rest after I left you, except that the punishment is reduced for me every Monday. He said: that was because the Prophet (blessings and peace of Allah be upon him) was born on a Monday and Thuwaybah brought the good news of his birth to Abu Lahab, so he manumitted her. 
“in bad shape” means in a bad condition 
“What happened to you?” i.e., after you died 
“After I left you, I never experienced any ease.” According to ‘Abd ar-Razzaaq from Ma‘mar from az-Zuhri, he said: “I found no rest after I left you.” 
“except that I was given to drink of this” this is also narrated in the original text, but in the report of ‘Abd ar-Razzaaq it is mentioned: “and he pointed to a indentation under his thumb.” This is an indication of the insignificant amount of water he is given to drink. 
This hadeeth suggests that the disbeliever may benefit from his righteous deeds in the Hereafter, but that is contrary to the apparent meaning of the Qur’aan, as Allah, may He be glorified, says (interpretation of the meaning):
“And We shall turn to whatever deeds they (disbelievers, polytheists, sinners, etc.) did, and We shall make such deeds as scattered floating particles of dust”
[al-Furqaan 25:23]. 
So our response is: 
Firstly, as the report is mursal, and ‘Urwah attributed it directly to the Prophet (blessings and peace of Allah be upon him) and did not mention the name of the one who narrated it to him, and even if we assume that it was mawsool (had a complete isnaad or chain of transmission), what the report speaks about is a dream, so it cannot be counted as evidence. Moreover it may be that the one who saw it had not yet become Muslim at that time, so it cannot be taken as evidence. 
Secondly, even if we assume that it is acceptable, it may be one of the things that apply only to the Prophet (blessings and peace of Allah be upon him), based on the story of Abu Taalib, as quoted above, which says that the punishment is reduced for him, so he was moved from the depths of Hell to a shallow part of Hell. 
Al-Bayhaqi said: What has been narrated about the invalidity of the disbelievers’ good deeds means that they will not be saved from the Fire and will not enter Paradise, but it may be that the punishment that they deserve for the sins they committed other than disbelief could be reduced because of good deeds they did. 
‘Iyaad, on the other hand, said: There is consensus that the good deeds of the disbelievers will not benefit them and they will not be rewarded for them with blessings or reduction of the punishment, although some of them will be more severely punished than others. 
I – that is al-Haafiz Ibn Hajar – say: This does not refute the possibility referred to by al-Bayhaqi. All the reports that speak of that have to do with the sin of disbelief (kufr); as for sins other than disbelief, what is there to say that they will not be reduced? 
Al-Qurtubi said: This reduction (of the punishment) is applicable only to this one and those who are mentioned in the texts. 
Ibn al-Muneer said in al-Haashiyah: There are two issues here: 
One of them is impossible, i.e., the idea that an act of obedience on the part of a kaafir could be valid in spite of his disbelief, because the condition of acts of obedience being acceptable is that they should be done with a sound intention, which is lacking in the case of the disbeliever. 
The second is rewarding of the disbeliever for some of his good deeds by the grace of Allah, may He be exalted. This is not impossible according to reason. But even if that is affirmed, Abu Lahab’s manumission of Thuwaybah was not accepted as a righteous deed. It may be that Allah showed grace to him as much as He wills, as He did in the case of Abu Taalib. And what matters is what is mentioned in sound reports.  
End quote from Fath al-Baari, 9/145-146 
And Allah knows best.