Brain Snacks: Tasty Tidbits of Knowledge
Frances Hodgson Burnett's younger son Lionel died when he was sixteen, and following his long illness and death, Burnett became deeply interested in the idea that you could communicate with the dead through meditation and psychic activity. Some of this belief in spiritualism might inform the whole Lilias-can-communicate-from-beyond-the-grave aspect of The Secret Garden. (Source.)
Frances Hodgson Burnett was also a believer in Christian Science, which teaches that prayer heals illness rather than medicine; this faith might also influence her representation of Colin Craven's illness as something that he can overcome through the power of positive thoughts. (Source.)