A world silver medallist in Beijing last year, Lapierre posted a jump of 8.21 meters to finish third behind winner Marquise Goodwin (8.42) and another American in Mike Hartfield (8.29) on Sunday.
It was the 32-year-old's fourth Diamond League podium of the year, having finished third in Rome and Shanghai and second last month in Rabat.
"I'm really confident," Lapierre told Australian media.
"I've been racking up the podiums and if I keep doing that, then going to Rio with the big stage, the momentum and the adrenaline, anything can happen.
"This is the best I've ever jumped in my life consistency-wise. When it comes to a major championship, I'm always going to lift.
"I've got two months to get stronger ... Once I do that, that's when I'll jump my jumps -- 8.40 and 8.50."
Lapierre, runner-up behind Olympic champion Greg Rutherford at last year's world championships, is hoping to be among the Briton's biggest threats in Rio.
He recorded his personal best of 8.40 back in 2010 and the Phoenix-based Australian felt he would have smashed that mark but for an error on his final jump in Birmingham.
"Instead of holding my hips up, I leant forward," Lapierre said of his error in flight, which he estimated cost him up to 30 centimetres.
"It would've been a really big jump."
Goodwin recorded the best jump of the year with his 8.45, a personal best, at Guadeloupe last month.
(Reporting by Ian Ransom; Editing by Nick Mulvenney)
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