Warren Gatland's side are preparing ahead of the first Test against Australia on June 22.
They kick off their campaign in the country later today against an under-strength Force side, which includes seven players who are yet to play Super Rugby.
Woodward said in his column in the Daily Mail: "It is unacceptable and disgraceful to cobble together a weakened, second-string club team to play against some of the best players in the world on one of the great rugby tours.
"Can you imagine Leicester inviting the All Blacks to Welford Road and putting out a second-string side? It simply would not happen. Treating the Lions with such contempt threatens to undermine their status in the global game.
"The Lions come to Australia once every 12 years but if this is how they are going to be treated in this country then they should seriously consider whether to return."
Woodward coached the Lions on their tour of New Zealand in 2005.