This is a really good question because on the surface it seems simple; however, it presents a real complexity. Exactly the kind of complexity Harper Lee wants the reader to contemplate. It could be argued that Tom Robinson tried to escape out of self-preservation, the human instinct to survive. Another argument could be he decided to take the chance, not human instinct but the luck of the draw mentality. Still another argument, although a man of integrity and honesty perhaps Tom redefined the meaning of those qualities to fit the jury's definitions of honesty and integrity. As sad as it sounds, Tom could only attempt his escape if he lowered his morality to that of the jury that convicted him.
Tom tried to escape because he knew that his situation was hopeless. Having been convicted of raping a white woman he knew that, having been convicted by a white jury, he had little or no chance for an appeal, regardless of what Atticus said. In Alabama at that time the sentence for rape was death, so he, in effect, committed suicide by trying to escape.
Because he is an innocent person.