It is my understanding that if someone dies in the state of mortal sin he will not go to heaven. What incentive do I have not to sin if I am already in the state of mortal sin?
The incentive not to sin always ought to be the desire not to offend God. Even if someone has fallen and committed a mortal sin, he should desire not to offend God any further. We live to serve him. Avoiding eternal punishment should be a side issue. He ought to come first.
The reason a person does not go to heaven if he dies in the state of mortal sin is that he is deliberately rejecting God and is choosing something or someone else as the ultimate object of his love. The Lord will never reject one who dies loving him. If he approaches death in the state of mortal sin and repents because he loves the Lord, the Lord will welcome him. Jesus endured Good Friday precisely because he loves us. Our incentive should always be to respond to his love. That is always appropriate for each and every one of us!