1) When the second day enters, we do not look upon the first day like a weekday. The Gemara (Beitzah 4b, five lines from the end of the page) states that nowadays we are expert at establishing the day on which the Hebrew month starts. The Gemara asks that, if so, why do we keep two days of Yom Tov in Chutz la'Aretz? The Gemara answers that the government might make a decree prohibiting the learning of Torah and the secret of when to add on an extra day to make a 30-day month will be lost (see Rashi DH d'Gazru), and we will no longer know when the real day of Yom Tov is.

Rashi (DH v'Avdinan) writes that it is a fixed law, through an enactment of the Chachamim, to keep two days even when there is no doubt about when the real Yom Tov is. We learn that the first day is Yom Tov is d'Oraisa and the second day is d'Rabanan.

2) I was thinking again about this question, and I remembered that there seems to be a slightly different way of looking at the first day of Yom Tov. Above, I implied that the first day of Yom Tov is certainly the real Yom Tov, while the second day is a Takanah d'Rabanan, which we know is not really Yom Tov. However, there seems to be another way of understanding the issue. This is to say that both days are a Safek. I am not aware of anyone who says that there is a possibility that the first day is definitely not Yom Tov, but I think we can show a source that the first day may be Yom Tov only out of a doubt.

The source is from the Sugya in Beitzah 4b, which appears immediately before the sugya I cited above. This is where Rav says that an egg laid on the first day of Yom Tov is permitted on the second day. Rashi (DH Muteres) writes that one of the two days is certainly a weekday, so the egg is clearly permitted.

Rashi implies that for either of the days there is the possibility that it is a weekday, which does not seem to be consistent with saying that the first day is certainly Yom Tov.

However, it seems to me that even if we say that the first day is only Yom Tov out of doubt, we still can answer the question on the Behag. We will say that even if one started the Mitzvah of Lulav only through a Safek, this is sufficinet to be able to say Shehechiyanu. The Berachah of Shehechiyanu, like almost all other Berachos, is d'Rabanan. Therefore, we apply the important rule of "Safek d'Rabanan l'Kula" -- on a doubt for a Rabbinical issue, we act leniently. Therefore, on the second night, the Shehechiyanu may cover the Lulav since it may be that the Mitzvah has already started.

3) I found that the Rosh in Sukah (4:2) asks this question. He writes: "Even if you want to say that the first day is a weekday, the Gemara states (beginning of 46a), "If someone makes a Lulav for himself he says Shehechiyanu and does not recite another Berachah (of Shehechiyanu) when he holds the Lulav. Here, too, he was Yotzei when he made the Berachah the day before, even if it is considered to be a weekday."

(The Rosh continues and writes later that since nowadays we are expert in fixing the new moon, the first day of Yom Tov is not in doubt at all, which was my first answer; see above.)

The point is that the Behag is referring to the Din of the Gemara that one says Shehechiyanu when one makes the Lulav, which is not what we do nowadays. We say Shehechiyanu when holding the Lulav. However, acording to the practice in the time of the Gemara, one may say Shehechiyanu on the Lulav before Yom Tov starts.

4) According to the conclusion of the Rosh, if one holds the Lulav in order to perform the Mitzvah, the Shehecheyanu applies even if said on a weekday:

a) Near the end of 4:2, the Rosh writes in the name of Rabeinu Shmuel of Evreux that nowadays -- when the custom is to say Shehecheyanu at the time of holding the Lulav (and not at the time of tying it) -- one should say the Shehecheyanu on the second day also, since the first day might have been a weekday. He writes that if one did not say the Berachah at the time of tying the Lulav but said it after the tying on the weekday, one is not Yotzei.

However, at the very end of his words, the Rosh writes a different line of reasoning. He writes that if one shook the Lulav on the first day -- even though it might be a weekday -- this is better than saying Shehecheyanu after the tying on a weekday, because in this case one shook it with the intention of performing the Mitzvah of Lulav.

The Rosh appears to be saying that even if it is really a weekday, if one says Shehecheyanu because one is intending to do the Mitzvah, this is a valid Shehecheyanu.

b) I think the Tur (written by the son of the Rosh), in Orach Chayim 662, explains this a little more. He writes that one does not say Shehecheyanu on the second day because one was Yotzei with the one that was said on the first day. He writes that this is not worse than if one said it at the time of tying the Lulav, in which case one is Yotzei.

It seems to me that the Tur is telling us that the Shehecheyanu on Lulav is an unusual Din. Since the Lulav is tied on a weekday, according to the original Din of the Gemara this means that Shehecheyanu for the Lulav is possible before Yom Tov starts. Therefore, nowadays that the Minhag is to say it when shaking the Lulav, it is also possible to say it even if one says that the first day is a weekday, because if the Shehecheyanu can be said on the tying before Yom Tov, since this is the preparation for the Mitzvah it can also be said on the first day when one intends to do the Mitzvah, even if it tranapires that Yom Tov has not yet started.

5) The Mitzvah of Lulav starts before Yom Tov begins:-

a) We have seen above something that I had not thought of at all when I started answering this question -- namely, that in principle a Shehecheyanu blessing that one says even before Yom Tov on shaking the Lulav is a Berachah that one can be Yotzei with, at least b'Di'eved.

It may be possible to understand this when we note that the Gemara (beginning of 46a) cites a Tosefta that when one makes a Lulav for oneself he says Shehecheyanu. Rashi (DH ha'Oseh) writes that this refers to one who makes the Lulav on Erev Yom Tov. This is because one may not tie up the Lulav on Yom Tov itself. Towards the end of 46a, Rav Ashi says that he saw that Rav Kahana said the Shehecheyanu blessing at Kidush. However, Rav Kahana was a late Amora but we do see that the original practice was to say Shehecheyanu on the Lulav before Yom Tov started.

b) We see that the Tur (OC 662) writes that if one said Shehecheyanu when shaking the Lulav on the first day, one is Yotzei even if one would say that this is a weekday, since it is not worse than saying it when making the Lulav before Yom Tov. Since the original source of saying Shehecheyanu is to do so before Yom Tov, it follows that one is Yotzei also if one said it when shaking the Lulav, even if this happened before Yom Tov started.

c) A similar idea is stated by Tosfos (Sukah 46a, DH Nichnas, who discusses Sukah, not Lulav). He writes that it is logical that since Sukah comes because of the Chag, its time to be Yotzei with the Berachah can even be on a weekday.

I suggest that the reason behind all of this is because of Simchah. Tosfos (Sukah 46a, DH ha'Oseh) writes that Chazal instituted a Berachah of Shehecheyanu for a joyous Mitzvah. According to this we can say that the preparation for a Mitzvah of Simchah, even before Yom Tov starts, is also part of the Simchah, so if one said Shehecheyanu then, it is valid.

Kol Tuv,

Dovid Bloom