The mishna quotes Rabbi Yosi (Suka 3:14) saying that if one carried a lulav in the public domain without thinking on the first day of Sukos which was also shabas it would not count as a violation of carrying between domains. The rationale in the mishna is that the carrier has an obligation to use the lulav and therefore is permitted to take it with him in that pursuit.
Ra'av clarifies that this permission only extends as long as the person hasn't discharged the mitzva of picking up [and shaking] the lulav and is on the way to doing so when moving it around outside. Since the required activity is picking it up, he justifies the possibility of pick it up without fulfilling the mitzva by holding it upside down.
משכחת ליה כגון שהפכו, שכל המצות כולן אין אדם יוצא בהן אלא דרך גדילתן שנאמר (שמות כו) עצי שטים עומדים, שעומדים דרך גדילתן
Here he is alluding to the opinion of Abaye quoted in the g'mara which says that all mitzvos must be performed using objects in the "manner" in which they grew. The prooftext is the command to build walls for the mishkan out of beams stood upright - in the direction they grew.
Later codifiers and commentators (e.g. in Orach Chayim 651:2) understand the application of the דרך גדילתן condition to mean that the point on the object that was formerly attached to the ground should be downwards, regardless of what its orientation was while attached. The Aruch Hashulchan (there) refers briefly to the opinion of the Ram"a that the point of attachment needn't be downward with respect to the ground, just with respect to the one holding it(?), and doesn't reject that logic. "דהקפידא היא שבידו יאחזם כדרך גדילתם. אבל מה שמטה אותם – אינו כלום"
Does derech g'delasan mean the-direction-in-which-the-plant-grew or upright? How do they know which it is, considering the small and strange set of precedents?