Gentle repose has three key bits of information that interact with a lich's rejuvenation. Relevant text follows.
Gentle Repose...
Duration: 10 days
You touch a corpse or other remains. For the duration, the target is protected from decay and can't become undead.
Lich's Rejuvenation...
If it has a phylactery, a destroyed lich gains a new body in 1d10 days,
There are no special rules about a lich's remains vanishing or turning to dust/powder on its destruction (wherein I would make an argument that dust qualifies as remains just like cremation would, plain-english), unlike the demilich- it still has a physical form and leaves behind remains when you destroy it. It doesn't gain a new body until its phylactery rejuvenation kicks in 1d10 days later.
A dead creature is a dead creature, not an undead one, until/unless it reanimates again, thus becoming "undead."
If you slay the lich, it rolls 1d10. In 1d10 days, its phylactery effect will trigger, reanimating it with a new body. If you wait six seconds after slaying the lich for it to roll 1d10, then cast gentle repose, by my reading, in 1d10 days the phylactery attempts to trigger, turning the dead creature back into an undead lich- but Gentle Repose denies the trigger.
The lich has not been slain a second time- the Rejuvenation trigger should not fire again. Rest in Peace?
It occurs to me that this is a very subtle, niche interaction, and probably wasn't RAI, but am I reading it correctly RAW?