Eduyos 2:10 lists several judgements which lasted for exactly twelve months:
חֲמִשָּׁה דְבָרִים שֶׁל שְׁנֵים עָשָׂר חֹדֶשׁ. מִשְׁפַּט דּוֹר הַמַּבּוּל, שְׁנֵים עָשָׂר חֹדֶשׁ. מִשְׁפַּט אִיּוֹב, שְׁנֵים עָשָׂר חֹדֶשׁ. מִשְׁפַּט הַמִּצְרִיִּים, שְׁנֵים עָשָׂר חֹדֶשׁ. מִשְׁפַּט גּוֹג וּמָגוֹג לֶעָתִיד לָבֹא, שְׁנֵים עָשָׂר חֹדֶשׁ. מִשְׁפַּט רְשָׁעִים בְּגֵיהִנֹּם, שְׁנֵים עָשָׂר חֹדֶשׁ.
Five things are twelve months: The judgement of the generation of the flood was twelve months. The judgement of Iyov was twelve months. The judgement of the Egyptians was twelve months. The judgement of Gog and Magog in the future to come will be twelve months. The judgement of the wicked in Gehennom is twelve months.
Some of these judgements are twelve solar months, while others are twelve lunar months:
1. Generation of the Flood: Rashi to Bereishis 8:14 writes that this was a solar year:
בשבעה ועשרים. יְרִידָתָן בַּחֹדֶשׁ הַשֵּׁנִי בְי"ז בַּחֹדֶשׁ, אֵלּוּ י"א יָמִים שֶׁהַחַמָּה יְתֵרָה עַל הַלְּבָנָה, שֶׁמִּשְׁפַּט דוֹר הַמַּבּוּל שָׁנָה תְמִימָה הָיָה:
"On the 27th [of the second month, the land dried]." Their descent [into the Teivah] was in the second month on the 17th of the month. These are the 11 days which the sun['s year] exceeds the moon['s year], for the judgement of the generation of the flood was a complete year.]
2. Iyov: Seder Olam Rabbah 3 expounds how we know this.
מכת איוב י"ב חדשים, שנאמר כן הנחלתי לי ירחי שוא ולילות עמל מנו לי (איוב ז ג), מה לילות למנוי שלהן אף ירחים למנוי שלהן.
The wounds of Iyov were 12 months, as it says (Iyov 7:3), "So have I been allotted months of futility, and nights of toil have been counted to me." Just as nights are according to their count, so, too, months are according to their count.
The term used in the passuk for month is ירח, a fairly uncommon term in this context. Normally it means "moon," which seems to indicate that this refers to a year of lunar months.
3. Egyptians: Seder Olam Rabbah ibid. demonstrates that it was twelve months based on the lunar calendar:
מכות מצרים י"ב חדשים, שנאמר ויפץ העם וגו' (שם ה יב), אימתי דרכו של תבן באייר, והם יצאו בניסן, לקו המצריים עשר מכות כל י"ב חדש.
The plagues in Egypt was 12 months, as it says (Shemos 5:12), "The people scattered [in all of the land of Egypt to gather stubble for straw]." When is it the way of straw [to be found]? In Iyar. And they left in Nissan. The Egyptians were stricken with ten plagues all twelve months.
As this exposition is based on Iyar and Nissan, it's clearly twelve lunar months.
4. Gog and Magog: Seder Olam Rabbah ibid. implies it's a solar year:
משפט גוג לעתיד לבא י"ב חדש, שנאמר וקץ עליו העיט וכל בהמת הארץ עליו תחרף (ישעיה יח ו).
The judgement of Gog and Magog in the future is 12 months, as it says (Yeshaya 18:6), "The kites will summer on them, and all the beasts of the earth shall winter on them."
I assume this is a solar year based on the inference from the seasons.
5. The wicked in Gehennom: This is clearly a lunar year, as evidenced by the practice of yahrtzeit being held on the same day of the lunar calendar, rather than the solar one.
The pattern seems to be that judgements of Jews are based on the lunar calendar while judgements of non-Jews are based on the solar calendar.1 The one outlier is the Egyptians,2 who were (obviously) not Jewish, yet were judged based on the lunar calendar. Why?3
1Cf. Sukkah 29a: "When the sun is eclipsed, it is a bad sign for the non-Jews, and when the moon is eclipsed, it is a bad sign for the Jews, for the Jews count by the moon and the non-Jews count by the sun."
2Whether Iyov was Jewish or not is established as a Tannaic dispute in Bava Basra 15b, so our Mishnah would accordingly hold like the opinion that he was Jewish.
3Obviously I will accept an answer that says that any of my assumptions or interpretations in this post are wrong, provided that it gives a coherent explanation of all five judgements, whether they are lunar or solar, and why.