A person maybe being addicted to something (you have nothing to go on beyond his word) does not in any way justifies unethical behavior. If he felt unable to control an addictive impulse he could have come clean beforehand with you, possibly end or pause the relationship on friendly terms until when/if he could bring this matter under control. The fact he instead lied and cheated shows that beyond any possible addiction he does not care nor respect you. There is no reason for you to remain in contact with this man.