He admits a combination of nerves and inexperience limited his chances four years ago, but now the 2005 Six Nations player of the tournament is ready to fight for his place against the All Blacks.
"I am a lot more confident than I was four years ago and I'm going there pushing for a Test spot," Williams told Wales on Sunday.
"I am four years older with more experience and confidence than I had the last time.
"Back then I wasn't really known outside Wales and was a surprise choice. I did feel that I'm not in this league four years ago.
"I was more hopeful about my position back then but now I know I can compete with these guys.
"I have grown up and have the experience of knowing what the Lions are all about."