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The Brazilian, who currently leads the inaugural Formula E championship, will join Ed Jones in the British team's line-up for the Canadian round of the series.
Piquet replaces Max Chilton at the wheel of the second car, the Briton competing in the Le Mans 24 Hours with Nissan.
"I'm really looking forward to my Indy Lights debut with Carlin," said Piquet. "I've been competing in a broad range of racing over the past few years and this will be another new experience for me.
"I love open wheel racing but haven't yet tried it in a US based series, so Toronto is going to be interesting. I can't wait to get in the car and see what we can do."
It will be the first time the former Renault Formula 1 driver competes in Indy Lights.
"In Max's absence we wanted another strong driver to help push the team forward," said team boss Trevor Carlin.
"We know that despite having no experience of the Indy Lights car, Nelson will push to the maximum from the start and that's what we're looking for this weekend.
"We've known Nelson since racing against him when he became British F3 Champion in 2004 and have seen many times since then his outright pace.
"He's shown in Formula E he's a master of street circuits and I'm excited to see what he and Ed can achieve together this weekend."
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