According to this statement, we can go through life without fully living it. Hence, "Life you may evade." I think whether a person truly lives life depends on the individual. For one person, it might mean taking risks and being adventurous. For another person, it might mean truly appreciating small moments and really investing in relationships. What Eliot is trying to say, I think, is that it is easy to get caught up in the day-to-day and not fully live life.
Death, on the other hand, cannot be avoided. This statement next to the statement about life just serves to make the statement about life that much stronger. We cannot avoid death, so it's so important that we don't avoid life because we don't want to die not having lived.
T.S. Eliot is implying that we can consciously decide not to partake of life to the fullest in certain areas. We may evade trying new things out of fear; we may evade getting proper education, training, mentoring to better ourselves to realize certain goals. In addition, we may evade forming new relationships out of fear of being hurt or of letting our true feelings and emotions show. In essence, we may take the easy way out of things - not putting forth the time and effort required to achieve certain goals. Our evading life is often out of fear, or worrying about what others think of what we are doing. Oftentimes we evade life because of a lack of confidence in our abilities and ourselves.
T.S. Eliot - Selected Essays
It would be interesting to know exactly how Eliot would define "life" in this sense. I would think he means living in a full, rich manner and being true to yourself and what you believe in. Those of us who simply go along with the daily rat-race may successfully evade that kind of life.
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.