Thanks for the info @willwade. Didn't realize the upstream was using Algolia. That's a shame IMO, as it leads individuals to rely on third parties when OSS can get them there free (one way or another), stymieing innovation as a result.
Regarding your second item, anyone having enough data to require something beyond Lunr probably isn't using this theme.
About upstream project, I'm not open to add more feature on that theme that may not exist on upstream project, but I'm trying to report at least everything feature (that seems relevant) from upstream project. That why Algolia support is tracked.
I'm sure Lunr I will check it but after Algolia, I can't work on both in same time (not enough time).
@willwade Thank for link I will check that. But as I said there is also new feature from Hugo 0.20 that should help.