If humans and all their songs are sad, then the skylark in "To a Skylark" is a creature of pure joy. As the speaker imagines it, this bird doesn't know anything about feeling old or tired or lonely. It is full of "delight" all the time, and its song is an expression of that happiness. Unlike people, it doesn't have to think about the past or the future, or lost love, or any of the other things that make us miserable. Lucky bird!
Although there is plenty of sad material in the poem, it is ultimately focused on the triumph of despair over joy. Hurray!
Hate to break it to you, but in "To a Skylark," joy and sadness are simply impossible to separate, and the poem shows us how one would be meaningless without the other.