(2-part post):
I've just checked my driving licence. It's an old-fashioned paper one (without a photo) but it doesn't include any form of 'title'. i.e. there's no 'Mr', 'Miss', 'Mrs', ''Ms', Dr', 'Prof', 'Lord' or anything else. The same is probably true of a photo-style licence.
So the only way you can have 'Lord' or 'Lady' on your driving licence is if it's actually part of your name. In the UK, anyone can call themself anything they like (as long as their is no intent to deceive). I can legally be 'John Smith' on Mondays, 'Amanda Jones' on Tuesdays, 'Darth Vader' on Wednesdays, 'Milly Molly Mandy' on Thurdays, 'Prince Nabooboo Diwanga the Third' on Fridays, 'President of the World' on Saturdays and 'Lord of a One Foot Square Bit of Land' on Sundays. I don't even need any form of documentation, such as a deed poll, but (obviously) some paperwork would help to convince official bodies (such as the DVLA) about the name I intend to use.
It would therefore be perfectly legal for me to call the one foot square bit of land I own in Scotland something like 'Muckshire' and call myself 'Lord of Muckshire'. (Once again, this assumes that there's no attempt to deceive anyone). However, I could still call myself 'Lord of Muckshire' without owning any land anywhere.