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Andrew Tod netted on Tuesday night, curling home a wonderful effort to bring Dunfermline level, in their draw with Partick Thistle.
But it was just their eighth goal from 10 league appearances and that inability to make the most of their chances has seen them draw six matches - including the last three - which is the most in the Championship.
When asked, prior to Saturday's goalless encounter with Livi, whether a striker coach coming in could help, Lennon replied: "I don't think that helps at all.
"What you end up doing is you make them overthink, or you give them too much information, or you start applying extra pressure that they don't need.
"You've just got to trust them and they've got to trust themselves. They've got pedigree at this level.
"Eventually, if we keep playing like that, we're going to give somebody a real beating, but I don't take the level of performance, or the approach or the mentality or anything, for granted."
While the match against Partick on Tuesday was an even game, Dunfermline failed to turn their superiority at Ayr and at home to Livingston into victories.
Only bottom side Queen's Park, who they visit on Saturday, with six, and eighth-placed Arbroath, with seven, have scored fewer than Lennon's men.
The boss had insisted: "It is clicking; I look at our level of performance over the last five or six games.
"Even when we got beat against Livingston, our first half performance was tops. Away at Arbroath, we should have won that one.
"It's okay me sitting here going, we should, should, should. We've got to just start turning the performances into wins.
"I can't ask any more of the players really. Their approach to the game, their conditioning, their football, their technique. the variation of chances we're creating, it's all there."
Lennon, who had said he felt Livi and Thistle were the division's two strongest sides, prior to Athletic's games with them, continued: "You just try and re-emphasise and analyse.
"You show them the clips and how well they've played and they've got to take a lot from it.
"There's no sort of singling out or anything like that. It's a collective, whether we win, lose, or draw.
"But, I'm just so enamoured with the level of performance. It's been so good, a really high level at this level.
"So, we've just got to try and maintain that, and keep their confidence high, and keep believing that they're doing the right things, which they are."
Although Dunfermline are draw specialists, they are unbeaten in seven games, have only lost once in this season's Championship.
Ahead of the Queen's match they lie fifth in the table, just one point outside the promotion play-off places, with a game in hand on the three teams immediately above them.