There seems to be several different takes on what influences a Patronus, which makes sense since the forms they take are never explained. Why loved one definitely play a factor, the take away point is that a Patronus (and Animagi forms) takes the shape of the animal that best describes your innermost, deepest personality traits, the part that is underneath disguises, life phases, and layers. Snape has virtually only one consistent positive trait…undying love for Lily Potter. After her death, Snape pledged his loyalty not to Dumbledore or Harry, but to her memory. His entire life since childhood has been impressing, courting, chasing, and dreaming about Lily. Snape loved Lily. This caused his Patronus to take the form of hers.Lily's Patronus was a doe, and Snape knew this. Snape was in love with Lily and always has been and so adopted the doe patronus. It also probably has something to do with the memory Snape uses to cast the Patronus. Most likely the memory has something to do with Lily. Lily's Patronus was originally a doe. After she dies, Snape loves Lily so much that his Patronus changes to that. . Since her image took up so much of his spirit, his Patronus match hers, though this is more to his admiration of her versus his own character. This is in contrast to Harry, who truly does have many strong traits that his father possessed along with paternal admiration. Lily’s Patronus meanwhile has nothing to do with Snape. She and James have extremely similar natures underneath their teen issues. Strong alpha leaders with great skills and flexible morals, very proud in their beliefs, and tireless fighters. These traits are associated with deer, hence why they share the same animal while remaining complementary. Snape's patronus represents his love for Lily; I interpret it as the intense will to complete a void. His patronus represents that precise type of suffering love. Another example: in 1996, Tonks' patronus becomes a werewolf because of her love for Lupin. Every patronus has a different meaning for his owner, and exists because of different reasons. While both Snape and Tonks felt a deep, difficult and troublesome love for someone, their patronus being that someone is like an attempt to closeness, as opposed to the real life unlikeliness or impossibility of that love relationship being trouble-free.
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