The kernels are all Ubuntu packages, and not related to Lubuntu. Being a flavor we have defaults that differ to Ubuntu Desktop, or Ubuntu Server (for releases of 20.04 in regards Ubuntu Desktop; we’re still identical to 18.04 Desktop & earlier), but that’s for new installs.
The 6.5 kernel was from Ubuntu 23.10, which is getting rather close to the EOL warning notices coming out (~six weeks before), thus as all prior LTS releases, the HWE kernel moves to the next release being 24.04 LTS.
I’ll refer you to Kernel/LTSEnablementStack - Ubuntu Wiki for more details, but a quick check, and you can see the next replacement already visible for 22.04 if you look
linux-image-generic-hwe-22.04-edge | 6.8.0-32.32~22.04.3 | jammy-proposed | amd64, arm64, armhf, ppc64el, s390x
That has been visible for a few days already; ie. the 24.04 LTS kernel that will be included on Ubuntu 22.04.5 LTS Desktop (including Lubuntu 22.04.5) ISOs. Installed systems upgrade to that before 22.04.5 ISO release though. There has been no change here (that I recall at least) for over a decade. It’s available first as the edge kernel for initial testing… before moving closer to actually being default for users.
The recommended release will change when the team (as a group) decides its time. Currently the LTS manual of Lubuntu still refers to the 22.04 manual, with STABLE being the 24.04 manual. We’ll change that too, when and as we’ve done in the past LTS releases too.
Of likely no interest, but I’ll provide the paste of all 22.04 kernels from my CLI enquiry.
linux-image-generic-hwe-22.04-edge | 5.15.0.25.27 | jammy | amd64, arm64, armhf, ppc64el, s390x
linux-image-generic-hwe-22.04-edge | 6.5.0.35.35~22.04.1 | jammy-security | amd64, arm64, armhf, ppc64el, s390x
linux-image-generic-hwe-22.04-edge | 6.5.0.35.35~22.04.1 | jammy-updates | amd64, arm64, armhf, ppc64el, s390x
linux-image-generic-hwe-22.04-edge | 6.8.0-32.32~22.04.3 | jammy-proposed | amd64, arm64, armhf, ppc64el, s390x
linux-image-generic-hwe-22.04 | 5.15.0.25.27 | jammy | amd64, arm64, armhf, ppc64el, s390x
linux-image-generic-hwe-22.04 | 6.5.0.35.35~22.04.1 | jammy-security | amd64, arm64, armhf, ppc64el, s390x
linux-image-generic-hwe-22.04 | 6.5.0.35.35~22.04.1 | jammy-updates | amd64, arm64, armhf, ppc64el, s390x