Dawson and company tackle a powerful Auckland outfit on Tuesday, then face the All Blacks next Saturday, knowing that defeat would consign them to a first Test series whitewash since 1983.
The England scrum-half has not featured in a Lions starting XV for more than three weeks, when New Zealand Maori inflicted a 19-13 loss on the tourists.
But he accepts that the final few days in New Zealand will stretch mental and physical resources.
"I am pleased to get a start, having not started a game since the Maori, so I am looking forward to it," he said.
"To be honest, I couldn't really care what game it is, I just want to start. It was getting to a stage where I was just sort of training to be on the bench, so I am really pleased to be involved.
"Of course, ultimately, the enjoyment of it on the playing side was to be part of a winning Lions Test series. That has not happened, but it doesn't mean the players have not enjoyed the tour. We've gelled superbly well as a bunch of players.
"Let's make no bones about it, this week is a very difficult week. All the players and all the management have had their hearts set on being successful out here, and really that means winning the Test series.
"In the bigger picture, it has been unsuccessful because we've not won the Test series," Dawson added.
"It is always going to be difficult. You can't lose perception of how rare a Test series victory is for the Lions, not just in New Zealand, but anywhere in the world. It is a very, very difficult task for the players and the coaches."
The Lions midweek combination, expertly coached by Ian McGeechan and Gareth Jenkins, are determined to make it five wins from five starts before returning home.
They've already seen off Taranaki, Wellington, Southland and Manawatu, although an Auckland side containing All Blacks Joe Rokocoko, Sam Tuitupou, Steve Devine and Brad Mika will take some stopping.
"The midweek team have been fantastic, culminating in a pretty awesome display against Manawatu. I think the performance they put in (against Manawatu) would have beaten most provinces that were in front of them," said Dawson.
"We are fully aware we need to be at that sort of level to win against Auckland, because they will be a lot better side than Manawatu and Southland, the last two sides the midweek team have played."
Several players, Dawson included, hope to press Test selection claims ahead of Sir Clive Woodward's scheduled team announcement on Wednesday.