It is alleged that Abu Thawr — not, Sufyan al-Thawri, the founder of the extinct Thawri Madhhab — stated that there is nothing wrong with female-lead mixed gender prayers, but his opinion on this matter is not documented to be at large; rather, under specific conditions. In addition, the majority of scholars disagree with his conclusion.
Background information
The person you are referring to in your question is Abu Thawr Al-Kalbi (Arabic: أبو ثور الكلبي). He was a scholar in Iraq, and was well respected among other scholars and the common people. He started off by giving fatwas based on his own opinion (i.e., using his own logic), but afterwards he reverted to using Qur'an and hadiths after studying under Imam Al-Shafe'i.
The opinion you are referring to is the one that is allegedly based on the hadith of Umm Waraqah in Sunan Abu Dawood:
حدثتني جدتي وعبد الرحمن بن خلاد الأنصاري عن أم ورقة بنت عبد الله بن
نوفل الأنصارية أن النبي صلى الله عليه وسلم لما غزا بدرا قالت: قلت له
يا رسول الله ائذن لي في الغزو معك أمرض مرضاكم لعل الله أن يرزقني شهادة
قال: قري في بيتك فإن الله تعالى يرزقك الشهادة
قال فكانت تسمى الشهيدة وكانت قد قرأت القرآن فاستأذنت النبي صلى الله
عليه وسلم أن تتخذ في دارها مؤذنا فأذن لها
قال وكانت قد دبرت غلاما لها وجارية فقاما إليها بالليل فغماها بقطيفة
لها حتى ماتت وذهبا فأصبح عمر فقام في الناس فقال من كان عنده من هذين
علم أو من رآهما فليجئ بهما فأمر بهما فصلبا فكانا أول مصلوب بالمدينة
Narrated Umm Waraqah daughter of Nawfal:
When the Prophet (ﷺ) proceeded for the Battle of Badr,
I said to him: Apostle of Allah allow me to accompany you in the
battle. I shall act as a nurse for patients. It is possible that Allah
might bestow martyrdom upon me. He said: Stay at your home. Allah, the
Almighty, will bestow martyrdom upon you.
The narrator said: Hence she was called martyr. She read the Qur'an.
She sought permission from the Prophet (ﷺ) to have a
mu'adhin in her house. He, therefore, permitted her [to do so].
She announced that her slave-boy and slave-girl would be free after her
death. One night, they strangled her with a sheet of
cloth until she died, and they ran away.
Next day 'Umar announced among the people, "Anyone who has knowledge
about them, or has seen them, should bring them [to him]."
'Umar, after their arrest, ordered to crucify them, and they were
crucified. This was the first crucifixion at Medina.
— Sunan Abi Dawud Hadith 591
Commentary on the hadith
In 'Awn Al-Ma'bood (Arabic: عون المعبود) by Muhammad Shams Aabadi (Arabic: محمد شمس الحق العظيم آبادي) said:
ثبت من هذا الحديث أن إمامة النساء وجماعتهن صحيحة ثابتة من أمر رسول
الله صلى الله عليه وسلم ، وقد أمت النساء عائشة رضي الله عنها وأم سلمة
رضي الله عنها في الفرض والتراويح
From this hadith, it is proven that a woman can lead the prayers of
her female community, based on the command of the Prophet (ﷺ). Aisha
lead the prayers among women, and so did Umm Salama in fard prayers
and in taraweeh.
— NOTE: My own translation, so treat with care.
He further added:
وظهر من هذه الأحاديث أن المرأة إذا تؤم النساء تقوم وسطهن معهن ولا
تقدمهن. قال في السبل: والحديث دليل على صحة إمامة المرأة أهل دارها وإن
كان فيهم الرجل فإنه كان لها مؤذنا وكان شيخا كما في الرواية، والظاهر
أنها كانت تؤمه وغلامها وجاريتها ، وذهب إلى صحة ذلك أبو ثور والمزني
والطبري، وخالف ذلك الجماهير
It appears from these hadiths that if a woman leads other women in
prayers, she stands among them, and not in front of them. He said in
Al-Sobol: And this hadith proves that a woman can lead her family in prayers, even if there were men amongst them, as there was one who
acted as her mu'adhin, and he was an old man as per the narration.
It appears that she [Umm Salama] used to lead him, her slave boy, and
her slave girl in prayers. Those who approved of a woman leading the
prayers as such are Abu Thawr, Al-Muzni, and Al-Tabari, and the rest
opposed this interpretation.
— NOTE: My own translation, so treat with care.
The commentary shows that a woman may lead the prayers among other women, or among a mixed gender within her household, and attributes this to Abi Thawr. The allegation that Abu Thawr said a woman may lead prayers among mixed genders at large is unknown where it originated from. I have come across some modernists claims that it is in Sunnan Al-Daraqutni, but I have not found anything to that effect in his book.
Authenticity of the hadith
For the sake of documenting the hadith used as evidence, it was mentioned in multiple books with two chains of narration that are quite similar. Most of the rulings are that it is da'eef, or hassan at best, which means it cannot be used to derive a rule.
The first chain of narration is:
'Uthman ibn Abu Shaiba
Wakee' ibn Al-Jarrah
Al-Waleed ibn 'Abdullah ibn Jumai'
Al-Waleed's grandmother (Laila bint Malik)
'Abdul-Rahman ibn Khallad Al-Ansari
Umm Waraqah
The second chain of narration is missing Laila bint Malik.
Al-Waleed ibn 'Abdullah ibn Jumai' — There is a difference of opinions among scholars about Al-Waleed ibn 'Abdullah ibn Jumai' (Arabic: وليد بن عبد الله بن جميع). His integrity in narrating hadiths is not the one in question, but rather his ability to memorize. Abu Hatim Al-Razi, Ahmad ibn Salih, Al-Dhahabi, Al-Waaqedi, and Yahya ibn Ma'een all consider him trustworthy. Abu Ja'far Al-'Aqeeli, Al-Hakim Nisapuri, Ibn Hajar al-Asqalani, and Al-Qattan did not authenticate his hadiths.
'Abdul-Rahman ibn Khallad Al-Ansari — 'Abdul-Rahman ibn Khallad (Arabic: عبد الرحمن بن خلاد) He is unknown.
Laila bint Malik — Laila bint Malik (Arabic: ليلى بنت مالك الأنصاري) She is unknown.
