I realize this is an old thread, but I'm curious about the answer. The original poster never answered the question of what "live deeply" means, leaving us to guess, so guess we must. Since he's talking about living deeply and death, I'm guessing his context is something like this "gatha" about impermanence by Buddhist monk Thich Nhat Hahn.
"The day is ending and our life is one day shorter. Let us look carefully at what we have done. Let us practice diligently, putting our whole heart into the path of meditation. Let us live deeply each moment and in freedom, so the time doesn’t slip away meaninglessly." http://mindfulgatha.wordpress.com/gathas/
I found a quote of his where he uses the words "live deeply" translated into French, "Le miracle, c'est de vivre profondément le moment présent." I learn from Wiktionary that "profondément" is derived from the Latin word "profundus" but I don't readily find an adverb equivalent to this adjective.
But even if you did find a Latin equivalent of "vivre profondément" I think those words alone remove it from the original context too much. What I think you really need is something like "Live deeply in the present moment, don't fear death." Or "Live deeply each moment, don't fear death." Though on the other hand, that might be too long for a tattoo.