The idea that one might evade life seems to me to suggest that not everyone is passionately or fully engaged in spiritual, professional, or emotional life.
People can turn away from experiencing the full range of sensations and obligations that life offers and in this way evade "real living".
For Eliot, I imagine that this phrase holds some spiritual significance as well as a hint at an idea of being honest enough to truly see one's life for what it is.
He was constantly confronting the sense of being "fallen" in life, of living in a world where people cannot touch true beauty anymore and instead grope after material things and after appearances.
What are the roots that clutch, what branches grow
Out of this stony rubbish? Son of man,
You cannot say, or guess, for you know only
A heap of broken images, where the sun beats,
And the dead tree gives no shelter...
His poetry is often an attempt to pierce this veil of appearances to see what lies beyond, what is real. This deeper reality, perhaps, is the life that is often evaded.