And while the 27-year-old desperately wants a winning start to the three-Test series, he readily acknowledges former Wales boss Hansen's role in allowing him such an opportunity.
"Graham (Henry) was the first coach who really picked me in the Welsh set-up, but I played more under Steve Hansen because Neil Jenkins played mostly during Graham's reign," said Jones.
"Steve was very honest from the start. He made things clear to me, he is quite straight, and he had a huge influence on me.
"We were a million miles away. Welsh rugby had fallen in terms of the international stage. We had success under Graham, whereby we had a 10 or 11-game winning streak, and after that, we came off things."
He added: "A lot of senior players retired, and suddenly we were just left there. Steve made things clear to us, regarding our fitness standards, our training, our working week and the way we lived our lives.
"Suddenly, he just opened our minds and explained things out to us. We had to get our backsides in gear to improve, and he brought with him Andrew Hore (fitness coach) and Scott Johnson (skills coach), which was superb.
"I would be delighted if we could win on Saturday, but obviously I owe Steve a lot and I respect him for everything he did for me, personally, and Welsh rugby.
"All I can say is that Steve got the team, and when he left the team, he left Welsh rugby in such a healthy state, compared to what he inherited."
Jones and half-back partner Dwayne Peel effectively clinched their Lions Test places by spearheading Wales' stunning second-half revival against Six Nations opponents France in Paris last February, a team performance Lions chief Sir Clive Woodward describes as one of the "best ever".
But now he has been handed the keys to number 10, Jones knows he must deliver as part of the Lions' midfield trio alongside Jonny Wilkinson and skipper Brian O'Driscoll.
"I was delighted with our Six Nations success, but that is in the past, and this is a new challenge for all of us," he said.
"Obviously, there is going to be pressure because you have been given responsibility to do a job, and you must do that job.
"But I have got so much faith in the players around me. There is so much talent out there, and there will be a lot of talking and input into the decision-making, so a lot of pressure is taken off you.
"It is a high-pressure situation, the first Test of a series, and for me and the majority of the players it is going to be the biggest game of our lives.
"But we must react under pressure and focus on the job in hand, which is to play rugby."
Jones will continue a long tradition of Welsh Lions Test fly-halves this weekend, emulating such heroes as Barry John and Phil Bennett who filled the jersey on previous tours to New Zealand.
"It is every youngster's dream to play for the Lions, but realistically as your career progresses, you just have different goals and aims," he added.
"For me, this season was about playing well for my club, and then I got picked for Wales. To be involved in such an enjoyable season with Wales and play the kind of rugby we did was very fortunate for me because it enabled Clive to pick me."
And of all the plans the Lions have in place, there is one code no All Black will be able to crack.
"Myself and Dwayne sometimes make calls in Welsh, although maybe Dwayne doesn't understand them sometimes!" revealed Jones.
"We've got a calling system in place, but now and again I might speak to Dwayne in a few words of Welsh."