Before I give you my answer, let's be clear about that dead animals mean. In Arabic it means Al-Mita الميته. The translation of the Al-mita is animals who die of old age, suffocation, physical torture (beating), falling out of height, or in a fight with another animal. Most of the animal fat these days does not come form such animals, but from animals that are slaughtered and killed in Abattoirs for meat, it does not make financial sense to seek such animals which usually are already eaten carcasses for their oils.
Also, as always, if you find yourself in need and the Mita is the only thing you have, you can always use it. In Islam dire need overwrites forbiddance.
Now to answer your question, Majority of scholars say it is forbidden as per the hadith says:
حَدَّثَنَا قُتَيْبَةُ، حَدَّثَنَا اللَّيْثُ، عَنْ يَزِيدَ بْنِ أَبِي حَبِيبٍ، عَنْ عَطَاءِ بْنِ أَبِي رَبَاحٍ، عَنْ جَابِرِ بْنِ عَبْدِ اللَّهِ ـ رضى الله عنهما ـ أَنَّهُ سَمِعَ رَسُولَ اللَّهِ صلى الله عليه وسلم يَقُولُ عَامَ الْفَتْحِ، وَهُوَ بِمَكَّةَ " إِنَّ اللَّهَ وَرَسُولَهُ حَرَّمَ بَيْعَ الْخَمْرِ وَالْمَيْتَةِ وَالْخِنْزِيرِ وَالأَصْنَامِ ". فَقِيلَ يَا رَسُولَ اللَّهِ، أَرَأَيْتَ شُحُومَ الْمَيْتَةِ فَإِنَّهَا يُطْلَى بِهَا السُّفُنُ، وَيُدْهَنُ بِهَا الْجُلُودُ، وَيَسْتَصْبِحُ بِهَا النَّاسُ. فَقَالَ " لاَ، هُوَ حَرَامٌ ". ثُمَّ قَالَ رَسُولُ اللَّهِ صلى الله عليه وسلم عِنْدَ ذَلِكَ " قَاتَلَ اللَّهُ الْيَهُودَ، إِنَّ اللَّهَ لَمَّا حَرَّمَ شُحُومَهَا جَمَلُوهُ ثُمَّ بَاعُوهُ فَأَكَلُوا ثَمَنَهُ ". قَالَ أَبُو عَاصِمٍ حَدَّثَنَا عَبْدُ الْحَمِيدِ، حَدَّثَنَا يَزِيدُ، كَتَبَ إِلَىَّ عَطَاءٌ سَمِعْتُ جَابِرًا ـ رضى الله عنه ـ عَنِ النَّبِيِّ صلى الله عليه وسلم.
I heard Allah's Messenger (ﷺ), in the year of the Conquest of Mecca, saying, "Allah and His Apostle made illegal the trade of alcohol, dead animals, pigs and idols." The people asked, "O Allah's Messenger (ﷺ)! What about the fat of dead animals, for it was used for greasing the boats and the hides; and people use it for lights?" He said, "No, it is illegal." Allah's Messenger (ﷺ) further said, "May Allah curse the Jews, for Allah made the fat (of animals) illegal for them, yet they melted the fat and sold it and ate its price."
Please note that the skin of the Al-mita is exclude per another Hadith:
أَخْبَرَنَا عُبَيْدُ اللَّهِ بْنُ سَعْدِ بْنِ إِبْرَاهِيمَ بْنِ سَعْدٍ، قَالَ حَدَّثَنَا عَمِّي، قَالَ حَدَّثَنَا شَرِيكٌ، عَنِ الأَعْمَشِ، عَنْ إِبْرَاهِيمَ، عَنِ الأَسْوَدِ، عَنْ عَائِشَةَ، قَالَتْ سُئِلَ رَسُولُ اللَّهِ صلى الله عليه وسلم عَنْ جُلُودِ الْمَيْتَةِ فَقَالَ " دِبَاغُهَا ذَكَاتُهَا " .
"The Messenger of Allah was asked about the hides of dead animals." He said: "Tanning it purifies it."
Which comes my opinion that if something from the Mita can be purified (like the above Hadith applied to the skin) can be used.
