Hi Thomas Schmitt, Thank you for fast feedback.
Have good day.
I can confirm recent experience, live CD couldn't boot UEFI but netinst could. I used live CD to boot a new machine and build LFS until the grub installation stage, when I discovered I couldn't install grub in UEFI mode because none of the UEFI kernel "stuff" was available, so then I had to boot netinst in UEFI mode, do a minimal Debian install to another USB key, boot THAT, and use that to install grub on the disk of the machine concerned, so I could get it to boot UEFI without re-doing the entire installation of LFS. Live is great in all respects except that one.
I've got to think UEFI capability on the live images can't be far away, since the netinst can already do it, and the number of machines that need legacy boot is dwindling all the time (although still large, I'll warrant) and there's a disturbing trend of new machines coming out with no legacy compatibility mode.
Mark