Whether or not England skipper Wilkinson should be on the plane has become British rugby's great debate.
Wilkinson, who has not played international rugby since his drop-goal won the World Cup in Sydney 17 months ago, is currently recovering from a second knee injury of the season.
A return to action is imminent - possibly when Newcastle tackle Zurich Premiership rivals Northampton next Friday night - and Falcons rugby director Andrew believes Woodward should not leave without him.
"I think he (Wilkinson) will be playing very shortly. His second knee injury is recovering well, and I think he will play before the domestic season finishes," said Andrew.
"Last season, after the World Cup, he had a long-standing neck injury - you just have to accept that.
"This season has been different. It has been a series of different short-term injuries, really - the biceps, then the knee injury against Perpignan that has been aggravated a second time.
"This season has just been a little bit unfortunate. There has been a toll of the last five or six years, definitely, and I think once this recovery period is over, I am sure he will be back to his best," Andrew told Radio 5 Live's Sportsweek programme.
"I would be very surprised if he wasn't picked for the Lions tour. There is a lot of talk about players being injured, and should or shouldn't they be picked, but the squad is so big.
"If a player is picked, and finds that he is ruled out after two weeks, they just pick someone else. To me, that's not a problem.
"The squad will probably end up being over 50 players by the end of the tour anyway, so I am sure he (Wilkinson) will be picked and they will have to take it week by week.
"I don't think they've got any choice, to be honest. It would be a slight risk if they pick him, as it would be with every other player who hasn't played a lot of rugby this season, but the Test series is at the end of June and first two weeks of July.
"That's what the Lions team is all about. It is about winning a Test series, and they don't play those Tests for the best part of another two-and-a-half months.
"It is almost half a season away, so there are tons of time between now and the Test matches."
If Wilkinson travels, then the All Blacks and any provincial side he features against will inevitably look to Test his physical state.
But Andrew says that such a scenario would be no surprise to England's record international points-scorer.
"It is Test match rugby, and people have tried to whack Jonny for the past seven years. Everyone who plays as an international fly-half and is a goalkicker and as key a player as Jonny is is going to get hit," added Andrew.
"It's nonsense to think anything else, it's nonsense to think it won't happen, and it's nonsense to think Jonny can't cope with it. It is part of being an international-class fly-half.
"Of course, they (New Zealand) will try to get hold of him and ruffle him physically and mentally, just like they've done with every other Test match fly-half in history."