After moving up to eighth place in the Scottish Premiership with wins over Partick Thistle and Ross County, Saints are looking to record three consecutive top-flight victories for the first time since December 2008, when Gus MacPherson led them to victories over Falkirk, Inverness, Kilmarnock and Hamilton.
Lennon's latest attempt to complete a treble ended in a 4-0 defeat by Dundee United last month, but the four victories from five games have given him encouragement that his side can shake off their inability to maintain winning runs.
Lennon said: "I certainly believe the consistency we have shown is the way we want to be. I have gone on in recent weeks about the inconsistencies that have dogged this football club for over 30 years now.
"I believe the players have the mentality to overcome that. That's about working hard for each other, taking care of the little things and showing the determination to turn the poor start to the season we had around, and to try to take us to where we want to be."
Lennon knows Hibs will be fired up after Butcher took over from Pat Fenlon during the international break.
Lennon said: "Hibs are going through a transition period. Pat assembled a very good squad and Terry will come in with his own ideas, his own training methods and his own style of football.
"How long that transition will take, we don't know, but knowing Terry, and with any new manager coming in, there is always a knee-jerk reaction with players going out there and giving him their all.
"The slate is wiped clean and everyone will be going out to impress.
"We must, and we will be, ready for that challenge."
St Mirren's impressive run of form has been partly founded on their youth policy with five academy players regularly starting in recent weeks. One of them, 19-year-old defender Jason Naismith, was rewarded with a new contract on Thursday that ties him to the club until summer 2017.
Lennon said: "He has come in and shown the true strengths he has. He worked very, very hard in the close season and he has become a real colossus of a young man.
"I know his father, George, well and he is a die-hard Buddies supporter so he will be a very proud man."
Butcher took over last week from Pat Fenlon who signed the 22-year-old striker for £200,000 from Swindon on a three-year deal in the summer.
The former Republic of Ireland under-21 player has only scored twice this season, against St Mirren and St Johnstone in successive weeks in September, and he "definitely" believes the best is yet to come after months of living off scraps.
Asked to sum up his start to his Hibees career so far, Collins was refreshingly honest.
"Not great" he said. "Obviously as a striker you want to score many more goals but on the flip side of it, there hasn't been many chances created for the strikers.
"Not just for me, for Paul Heffernan, Rowan Vine and Ross Caldwell, so if that can change and if balls go in the box and we are still not scoring then we have to look at ourselves.
"Goals is a massive thing and we need to score more.
"If I get the nod against St Mirren, hopefully I can repeat my performance (from the first game).
"I want to score a lot more goals and for the team to finish in the top four, let alone the top six.
"If we can get a European place then it would be brilliant.
"We have got a good set of players here and if we get at teams from the off instead of going behind and then playing well, not many teams in the league can live with us."
Collins insists the Hibernian players "are raring to go" against the rejuvenated Buddies who can leapfrog the seventh-placed visitors with a win.
He said: "The boys are looking forward to it. Saturday can't come quick enough and I can't wait.
"A new manager comes in with different ideas and you have to adapt to that as quickly as possible otherwise you won't find yourself in the team.
"So it is down to you to concentrate and work hard and hopefully the rest of it will take care of itself.
"The gaffer said it was a fresh start for everyone and everyone has been looking sharp and wanting to show him what we can do."
- Sports & Recreation
- Pat Fenlon
- Terry Butcher
- St Mirren