With Woodward due to name his 44-man party on Monday, Evans believes that a sense on unity will be key to the success of the tour.
He said: "One of the key aspects of the Wales Grand Slam team, which the Lions need to take on board, is unity and total unselfishness.
"It was the team cause above everything else and that is what the Lions want to take out of this. Together, the sum total exceeds individual parts.
"On tour for nine weeks you need to enjoy your rugby. Speaking to the Wales Grand Slam players, it was quite a liberating experience.
"They were allowed to express themselves. In a day where so much is pre-ordained, it is quite refreshing to see that attitude."
This, according to Evans, is the key to avoiding similar performances to the 1993 defeat in New Zealand and the series defeat by Australia four years ago.
He added: "2001 was so disappointing in so many different areas. It was how not to do things, they will have learned from that.
"It is not always about training twice a day. You are talking about quality players. They know what to do. It's about balance and being able to gel as a squad."