Question: Why can you hold your lulav and esrog during davening, including shema and shemone esray but you can’t hold your tefillin in your hands, or a knife , plate full of stuff, or bread, neither can you hold your lulav and esrog while learning Torah, what is the difference?
A. Rashi in Sukkah 41b says you’ll be afraid the knife will fall on your foot, the plate full of stuff will spill, and if the bread falls it will become disgusting. But if the lulav and especially esrog falls it might become unkosher?
B. Love for the mitzvah not a burden
C.תלמוד תורה כנגד כולם
Answer: The taking and holding of the lulav and esrog is the mitzvah and because of the love to perform the mitzvah it is not considered a burden therefore you won’t be distracted during davening but holding tefillin or the knife, bread and plate is a burden and will be a weight and distraction during davening which will not allow him to concentrate properly. By Torah learning since he will get so involved in his learning and will get distracted from the mitzvah of lulav and esrog and they might fall out of his hands therefore he should give it to someone else to hold while learning. (See Rashis there.)