I frankly have no idea what this song means but I'll give it my best shot. I believe the "Lily" in the song is a part of Stevie (as it is in the song Rock a Little), a part of her that has been lost somehow - is it the child-like part? I guess so, because she keeps talking about a "baby" that she's searching for. However, because she constantly trying to rediscover that part of herself, she's never satisified with the way she is, or with her life.
This frustrates "the man [she] loves" because she is spending her life searching instead of living in the present. He won't stand in her way, though, because he can't. He "knows how important" her search for her inner self is to her. Still, he can't help but feel bitter that the search seems more important to her than him, thus the "search until you die!" proclamation. He's saying, "Go ahead, waste your time, I won't stop you, but it's an 'impossible task' to find what you're looking for." She assures him that she's not choosing the search over him, that she'll come back to him when she's found what she's looking for, and she wants him to wait for her - but does he believe her? As for her, she'll never be satisfied, but she has to keep trying.
This is my own interpretation of this wonderful song and maybe Stevie wanted to say something completely different . I may be absolutely wrong .
I guess the song is about Robin . If Stevie has written it before 1982/83 I'm really wrong . But I think she might have written it after Robin's death .
When I look at you , I see me might show that Stevie and Robin were really almost reflections and best friends . Lily is Stevie , she used to call herself like that as she said in an interview (I hope I remember right) .
It's sad that you never even know me . This might as well be about Robin (who maybe loved Stevie though she never completely understood her) or about someone else (maybe Lindsey who possibly did not understand what Stevie felt for Robin) .
The impossible task after Robin's death was taking care of her baby . Stevie thought she could manage it by Kim , Robin's husband , which did not work . Stevie knows that she has failed terribly (and Kim nowadays doesn't talk to her , they have not met after their divorce) , but it was Robin's last will and she has to search on though everyone believes/knows she will not make it and she will search until she dies , even the man she loves . It could be Lindsey as well as somebody else , but somebody who knows her good enough .
When she was married to Kim , she just had no more strength and wanted to come home . But she stayed , no matter what the price was . Maybe Robin was still her guiding light (there you were in all this glory) . The man she loves (I really think it's Lindsey , but as I said it might be somebody different) discourages her . He just knows it's impossible to make Robin's last dream come true . But Stevie cannot stop . She wants to see this thing through . She wants to find this baby .
I try to be very careful regarding my thoughts on She was not my first one , but he was my last one . Maybe Stevie tries to find a sensible reason to give up . Robin was not her first friend , but Lindsey (I'm really sure it's him) will be the last one in her life (= she regards him as very , very important) , and so it would be better to do what Lindsey advises her to do . It's breaking her heart not to be able to do what Robin wanted her to do , but she needs to break out of this marriage with Kim . She will still search on - she will come back when she can , but now she needs to go back .
Maybe the part And the lady walks up to him and says I'm leaving again is about Kim . She is the lady who was part of his life for a while , but now she's leaving again because it's too hard for her .
The part Don't you need more ... don't you need more of you and me (which is my favorite part) might be addressed to the world . She wants to show the world that there should be more people who have such a wonderful friendship as she had with Robin .
The last part is again her explanation that she will search on , though the man she loves said she can't . She has broken out of her marriage with Kim, but in her heart she will always be with Robin and her dream .
In my opinion , this is the saddest story Stevie has ever told in her songs . City Of Hope is also about Robin , but as the title says , there is hope . In this one there's no hope . I think this story is incredibly sad - she cannot make her best friend's last dream come true and it will always haunt her . She doesn't really care what the man she loves says , she doesn't care if she can take it , she has to do what Robin wanted her to do and she will try it until she dies .
This one is actually very easy and very literal. Just like her song "Julia", "Impossible Task" is Stevie reinterpreting her & Robin's lives through the movie JULIA, starring Jane Fonda & Vanessa Redgrave. In the Mary Turner interview in 1986, Stevie said how that was one of her favourite movies, and Stevie
was Lily, and Robin was Julia.
In the movie (based on a true story), after many tribulations & heartaches, after Julia dies, Lily decides to raise her only child. The movie is a complicated study of friendship, but it really explains the story behind "Impossible Task".