What is incumbent upon a person who vowed to fast on Mondays and Thursdays for life, but forgot the condition for the vow to take effect and to fast for seven years? Is he obligated to make up for these years?

Going to a conditional vow (nazr mu'allaq) is disliked (makrooh) and changes nothing of Allah's decree. It must be fulfilled if the condition attached to it is met. However, if you did not fulfill it believing that the condition was not met, then there is no sin upon you. You are not obligated for anything concerning the past seven years in which you did not fast on Thursdays and Mondays, because you are excused due to forgetfulness. For a specified vow (nazr mu'ayyan), if it is missed due to an excuse like forgetfulness, there is no expiation (kaffarah) or making up (qada').