In tafsir ibn Kathir this is quoted without any reference in the interpretation of verse 11:77:
Allah, the Exalted, informs about the coming of His messenger angels. After they informed Ibrahim of their mission to destroy the people of Lut, they left him and set out to destroy Lut's people that very night. After leaving Ibrahim, they came to Lut. Some say that they came to him while he was on a piece of land that belonged to him. Others say that they came to him while he was in his home. They approached him while they were in the most handsome of forms. They appeared in the forms of young men with handsome faces. This was a test from Allah that contained much wisdom and a firm evidence. Their appearance saddened him (Lut) and he felt grief in his soul because of them. He was afraid that if he did not host them as his guests, someone else of his people would host them and harm them. (source: qtafsir)
As these Prophets have been earlier visiting Ibrahim as stated in the Quran (at least this part of the story can be found a few verses earlier) and as many tafsirs say. I searched in the verses telling the encounter betwen Ibrahim and the Angels which is quoted in suart hud (11:69-76) and their I found this quote in tafsir ibn Kathir, who is quoting a statement of as-Suddi (a Mufassir from the time of the tabi'yn who died 127 a.H. there's a short Wikipedia article about him in German), while interpreting:
But when he saw their hands not reaching for it, he distrusted them and felt from them apprehension. They said, "Fear not. We have been sent to the people of Lot." (11:70)
(and conceived a fear of them. ) As-Suddi said, "When Allah sent the angels to the people of Lut, they set out walking in the form of young men, until they came to Ibrahim and they were hosted by him. When Ibrahim saw them, he rushed to host them. (source: qtafsir)
So young men is quoted by as-Suddi.
This is also in tafsir at-Tabari (while interpreting verse 11:71)
...And his Wife was standing, and she smiled. ...
who quoted an own narrator chain:
18314 - حدثني موسى بن هارون قال ، حدثنا عمرو بن حماد قال ، حدثنا أسباط ، عن السدي قال ، بعث الله الملائكة لتهلك قوم لوط ، أقبلت تمشي في صورة رجال شباب ، حتى نزلوا على إبراهيم فتضيفوه ...
I heard from Musa ibn Haroon (who heard) from 'Amr ibn Hammad from Asbaat from as-Suddi who said: (as quoted by ibn Kathir)
and on the authority of Wahb ibn Munabbih (I'll quote only the necessary part):
18319 - حدثني المثنى قال إسحاق قال ، حدثنا إسماعيل بن عبد الكريم قال ، حدثني عبد الصمد أنه سمع وهب بن منبه يقول :
I heard from al-Mothanna (who heard) from Ishaaq from Ismael ibn Abdulkareem from Abdussamad (ibn Ma'qil if it is the same as in the following narration) who heard Wahb ibn Munabbih saying:
لما أتى الملائكة إبراهيم عليه السلام فرآهم ، راعه هيئتهم وجمالهم ،.
When the Angels came to Ibrahim peace be upon him and he saw them he was delighted by their beauty and appearance. ...
Ibn Abi Hatem (Here also a German Wikipedia article is available, beside the Arabic one) also quoted in his tafsir a similar narration:
 أخبرنا أبو عبد الله الطهراني -فيما كتب إلي-، ثنا إسماعيل بن عبد الكريم ، حدثني عبد الصمد بن معقل قال: سمعت وهب بن منبه فلما رأى الله ذلك يعني: فاحشة قوم لوط بعث الله عز وجل الملائكة ليعذبوهم، فأتوا إبراهيم فلما رآهم راعه هيئتهم وجمالهم، فسلموا عليه وجلسوا إليه، فقام ليقرب لهم العجل، فقالوا: مكانك قال: بلى دعوني آتيكم بما ينبغي لكم، فإن لكم حقا لم يأتنا أحد أحق بالكرامة منكم، فأمر بعجل سمين، فحنذ له يعني شوي، فقرب إليهم الطعام، فلما رأى أيديهم لا تصل إليه نكرهم، وأوجس منهم خيفة وسارة وراء الباب تسمع.
Note that ibn abi Hatem says that the he was informed by abu Abdillah at-Tahrani whom wrote to him this narration with the given chain (in bold letters the similar narrators of at-Tabari, and the important part of the statement)
So we learn from this that the source for their handsome appearance is this statement of Wahb ibn Munabbih, I didn't check whether there are other sources!