sickly rainbow, what does it mean?

to read a thousand stormy gales,
and sing of cats and great blue whales;
to lose a girl you've not for fought,
to lose a man you need say naught!

with cheerful skies that heavy rains, a rainbow sickly sorrow sweet,
alas, this world's too beautiful, so in another we might yet meet.

p/s: double post because i feel like it!