The Buddies go into Sunday's clash with Hearts at Hampden Park as underdogs but Lennon is quick to remind their critics that they were written off in the previous two rounds of the competition.
But they followed up a penalty shootout win at Aberdeen in the last eight with a 3-2 success over Celtic in the semis.
"You never know how they are going to be on the day but the experience they had in the semi-final will help," said Lennon.
"We know it's going to be a bigger crowd and there will be an absolutely terrific atmosphere.
"A lot of players throughout their career will not get to a final at all. For some of our players this might be their only cup final, for other ones it may be the start of many for them.
"My message come Sunday will be to make sure they make it an occasion that lives long in their memory for the rest of their lives and don't waste this opportunity.
"We have certainly earned the right to be here. A lot of people didn't expect us to go and beat Aberdeen up at Pittodrie.
"Everyone wrote us off in the semi-final against Celtic but we brought our true qualities out on that day.
"But that doesn't give us any right to lift the cup on Sunday.
"The team that earns the right to lift the cup on Sunday will be the team that works the hardest and brings out their true qualities on the day.
"The true strength of these players is when they believe in themselves and believe in one another, when they work together and bring out their key strengths.
"When they do that, we are more than a match for anyone."