It works on some devices; they do sign the builds as far as I can tell. But the bootloader itself needs to be convinceable to trust the LOS signatures, and needs to understand the secure boot implementation used in the Android that the current LOS is built from (since Android has re-done it all a few times). Nobody knows anything about bootloaders to figure out which of them can do this or how they would be induced to do it.
It works on some devices; they do sign the builds as far as I can tell. But the bootloader itself needs to be convinceable to trust the LOS signatures, and needs to understand the secure boot implementation used in the Android that the current LOS is built from (since Android has re-done it all a few times). Nobody knows anything about bootloaders to figure out which of them can do this or how they would be induced to do it.