The Gemara (Pesachim 109a) says that when the temple was standing, the only way to achieve simcha (loose translation: “joy”) on the holidays was to eat meat (from the sacrifices). Today (when there is no temple), the only way to simcha is through wine.
Back then it was an obligation to eat meat on the holidays. Today, it is not an obligation, but it is still a mitzvah (Biur Halacha, Siman 529, d”h keitzad mesamchan).
There is a tradition on Shavuot to eat dairy products. We find it codified by the Rema (Rav Moshe Isserles) in Orach Chayim 494:3 as follows:
ונוהגין בכמה מקומות לאכול מאכלי חלב ביום ראשון של שבועות ונ”ל הטעם שהוא כמו השני תבשילין שלוקחים בליל פסח זכר לפסח וזכר לחגיגה כן אוכלים מאכל חלב ואח”כ מאכל בשר
(My translation): And there is the tradition in some places to eat dairy foods on the first day of (the holiday of) Shavuot, and it seems to me that the reason is that is like that it should be like the two dishes that we eat on the first night of Pesach, (one in) rememberance of the Passover offering and (one in) rememberance of the festival offering, so to (on Shavuot) we eat dairy food and afterwards meat food.
To recap the most important part: it is perfectly fine to have some cheese cake and lasagna on Shavuot. Just be sure to follow it up with some nice bassar (in that order)!
June 8th, 2005 at 8:38
Incidentally, the German minhag is to have a completely dairy lunch on the first day of Shavuos, not followed by any meat. There is a meat meal for lunch the second day.
Perhaps the interpret the afterwards as being WAY afterwards.
June 8th, 2005 at 9:23
The Rema makes an analogy between the two dishes that are eaten on Pesach, one in memory of the festive offering and one in memory of the Passover sacrifice. When the temple was standing, an we were performing these sacrifices, the festive offering was eaten as the main part of the meal on the first night of Pesach, with the Passover sacrifice coming at the end (achilah al hasovah) where we eat our affikoman today.
The Rema uses these dishes (definitely eaten in the same meal) as the model for eating two dishes (one milk, one meat) on Shavuot. So if you accept the Rema’s reasoning, I think that they have to be in the same meal. (I would guess that the minhag evolved in many communities to have dairy on one day and meat on the second simmply because of the logistical difficulties and potential for mixing milk and meat that would result from having both dishes at the same meal).