You’ve not provided any release details; and if it was a recent LTS release for example the ISO details matter (eg. Lubuntu 22.04.2 LTS has a later calamares or installer than the earlier Lubuntu 22.04 media; so the .2 detail is useful).
You mention it booting on another box as your test; if that other box has different hardware - the test is only 100% useful if you also jumped to terminal & confirmed the media validation completed successfully in my view. How you check the media varies on unspecified release, but you mention grub 2.06 which would imply you’re talking about 22.04 or later possibly.
How long did you wait? Some boxes have firmware that can cause live media to be very slow to boot; eg. on this thread I talk about hardware that can show blinking cursor for 7+ minutes (longer on some ISOs too), but you gave no timings. Whilst you can write the ISO to thumb-drive to speed this up, as it only impacts the live media which we use to install Lubuntu with, I suggest just writing the ISO normally & install; as boots of the installed system aren’t slow.
You didn’t mention how you wrote the ISO to your thumb-drive; it’s possible to write an ISO so it’ll boot only on some hardware systems (eg. booting on uEFI only, but not older BIOS boxes, or the reverse), so I usually opt for CLONE writes which will boot on all.
That’s my reaction anyway… With more detail I maybe able to offer more. Even hardware details can be helpful; as I have no idea what you consider ‘old’; all my hardware is refurbished, so even my ‘new’ hardware maybe something you consider ‘old’.
FYI: For some clues on media checks; this prior comment of mine maybe helpful if you wish for some details.