What are reasons why christians should try to live a moral life?

The most important reason is because they want to be admitted into Heaven when they die.

According to Christianity, if you are a good man throughout your life, that goodness will be repaid when you die. If you didn't commit any crimes, then you have nothing to fear - you will be able to enter Heaven and live the rest of your days there, in bliss. Also, Christianity teaches people to love the people around them, not to commit crimes, not to think evil of others, etc. in order to lead a happy and moral life.