Need your help.

I have a 2003 nissan altima with a 2.5s engine automatic trans. With 94,000 miles. When I turn my engine on in the morning it does it fine, when I put my car in drive it jumps on me as if though it wants to turn off on me. When im driving down the road from time to time if feels like my car wants to turn off on me and it does sometimes but only when im coming to a stop. I changed my upstream oxygen sensor but not my downstream sensor I did a scan on it n it shows that my downstream is running lean, can this be the cause of my problem or can I be having another one, I had a trouble code p0420. I believe the the problem is with the oxygen sensor. By me letting the car run in this way can I damage the cat. Converter. Thank u 4 ur help.