My wife observed a young man in shul after davening acting very gentlemanly by handing his lulav to his kallah-to-be in the ladies' section so she could fulfill the mitzvah of netilas lulav. My wife immediately turned to me and raised a halachic red alert: did the kallah-to-be just become the kallah!? It's five months until Purim, but my wife remembered the Rama (O.C. 695) that says a man should not send mishloach manos to a single woman lest it be taken as an indication that she is mekudeshet to him. The same should apply to the mitzvah of lulav.
There is, however, a difference between lulav this year and mishloach manos. Mishloach manos is a gift which is meant to be kept; a lulav (on all days except the first) is merely borrowed for use to fulfill the mitzvah. Additionally, it is not that we suspect the mishloach manos of being used for kiddushin -- the suspicion (see M.B.) is that the kiddushin already took place and the mishloach manos are engagement gifts (sivlonos) after the fact. While mishloach manos are indeed meant as gifts, a lulav is not.
All that being said, the Halichos Beisa concurs with my wife and recommends that a man avoid giving his lulav to a single woman. Be careful who you lend your lulav to -- you may be getting more than you bargained for!
(For those who are already married, there is another halachic problem that comes up when we perform the mitzvah on the first day of Sukkos. On the first day only the mitzvah must be "lachem", meaning you must own, not borrow, the lulav and esrog. However, the halachic rule is "mah she'kansa isha kansa ba'alah" -- a woman has not independent ability to acquire property or goods; whatever she buys or takes possession of belongs to her husband. How then can she ever acquire her own lulav and esrog? Whether mah she'kansa isha... blocks kinyanim on a d'oraysa level and if it does how and whether we need to circumvent it is a discussion for another time, as it is a non-issue this year. See the notes at the end of the Bikurei Ya'akov.)