Gatland does not wish for a repeat of the media circus that sprang up around England's 2011 Rugby World Cup campaign, in which off-field antics dominated the headlines.
However, Ashton believes that the players involved in the New Zealand incidents have learned from their mistakes and are now more responsible.
"The people who were around then have learned their lessons from that and the people who weren't there know the consequences if you get involved or caught out in the way we did, so I don't think there'll ever be a repeat of that," PA quotes him as saying.
"At the time, it was a mistake and it was something we didn't intend to happen.
"We didn't do it on purpose but sometimes it takes mistakes like that for you to learn and luckily the guys who have come into the squad have seen those mistakes we made."
The Lions' first Test clash against Australia will be held in Brisbane on June 22.