I'm going to lie to my new partner about my affair
Why do you want to lie about your affair?
I don't want him to find out about it and feel bad
In a relationship it is expected that you would be faithful to your partner. Lying to them could erode the trust you have and ruin the relationship.
Lying to him is the only way I can get away with it.
You should either end your affair immediately or break up with your partner. There is no in between. Your partner is going to find out about your affair eventually so you should stop lying to him.