The Inhaler frontman - who has followed in his famous dad's footsteps by embarking on a career in music - admitted he found himself completely starstruck when he met The Strokes singer.
He told the Daily Star newspaper's Wired column: "As a band, we worship The Strokes.
"Growing up, I've been around some crazy, mad people are idols. I don't usually get starstruck, but seeing Julian Casablancas was a whole different ball game."
Eli revealed the pair met when he was out shopping for a new jacket to wear during a gig that night, and he bumped into his hero.
He explained: "The day we played a show in London just before lockdown, I bought a brown leather jacket to wear on stage.
"As I left the shop, I looked up to see Julian walk right by me. We locked eyes for a second, I froze up. I couldn't move!
"Julian looked at my jacket and said, 'Hey, nice jacket.' That's the most starstruck I've ever been."
Meanwhile, the Irish musician - whose band released their debut album 'It Won't Always Be Like This' on Friday (09.07.21) - admitted he is "disappointed" in groups who don't write their own material.
He said: "I'm always disappointed when I hear a song sung so well to find they didn't write it themselves.
"It's a shame so much music these days is written by ghostwriters. It's important people realise our album is something we've created, rather than take someone else's idea."
His bandmate Ryan McMahon agreed, as the drummer insisted they didn't feel the need to add anyone to their writing process.
He admitted: "Four friends is enough to write with. If we had a fifth brain in there, we'd argue too much and songs would never get written."
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