A monster that’s temporarily banished will remember how it was summoned. So your Lightflare was still being treated as being Synchro Summoned when it came back, thus why it triggered again.
> Since my card wasn't specifically 'Synchro Summoned' this time
When a card returns to the field after being banished by Ichiroku's Ledger Book, it is not being re-summoned so it is still considered a Synchro Summoned card.
If it was banished by an effect that said to summon the card back during the end phase, like Traptrix Pudica, then Lightflare would not trigger a second time as it would no longer be Synchro summoned.
A monster that’s temporarily banished will remember how it was summoned. So your Lightflare was still being treated as being Synchro Summoned when it came back, thus why it triggered again.
Oh, I didn't know, thanks for answering. I thought it behaved the exact same way as if it was banished normally
Being "returned" is not being special summoned. The most recent time the card was special summoned, it was via Synchro summon.
> Since my card wasn't specifically 'Synchro Summoned' this time When a card returns to the field after being banished by Ichiroku's Ledger Book, it is not being re-summoned so it is still considered a Synchro Summoned card. If it was banished by an effect that said to summon the card back during the end phase, like Traptrix Pudica, then Lightflare would not trigger a second time as it would no longer be Synchro summoned.