This term is used to describe a man who is utterly overwhelmed by insignificant circumstances and who often proclaimes his discomfort loudly and expects others to sympathize with his circumstances.
Jenny: Hey Alice I haven't seen your husband today. Is he alright?
Alice: he's fine he just drank too much last night and he's really hungover. He's been in bed all day and I have to wait on him hand and foot.
Jenny: Wow, he's such a wilting Lilly.
Fred: hey Bill would you like to go fishing today?
Bill: no Fred there's a 10% chance of rain today and I don't want to risk getting pneumonia.
Fred: Geez Bill aren't you the wilting Lily.
See also:
Pussy
Pansy
Buttercup
Millennial