The 25-year-old came off the replacements' bench at Northampton on Friday to play 50 minutes in the Falcons' 23-22 Zurich Premiership defeat after overcoming medial knee ligament damage.
And Wilkinson is growing in confidence that he will win his race against time and travel with the Lions, telling the Daily Mail: "I'll be there."
He added: "Clive has given me something to prove. I am comfortable that I have to earn the right to be in the squad.
"I promise people I will fight and work as hard as I can. That is what makes me proud as a person."
Wilkinson did, however, admit he picked up another niggling neck injury in his comeback match, but played down its seriousness.
He said: "It is just something that happens when you are getting used to things again.
"I took a bit of a hit on my head. Steve Thompson went to kick the ball in front of me and I went to grab it. He kicked it and also me.
"I woke up in the morning and thought I needed to do things properly. Perhaps after my first game back it was better to have a little rest."