I think hyperthetically, the answer is yes. As to the question as to how you would go about it if you really wanted to do it, you would have to ask the CAA. Because it has probably not been done before, they will be thinking on their feet which means the answer would be different depending on who you ask, and what sort of mood they are in depending on whether they have just had lunch/enjoyed their coffee/got laid last night.
If I was that person in the CAA and being asked, I would say the sensible and logical answer is that if someone did want to fly a Learjet on a PPL, they should show a level of knowlegde to ATPL standard (as that is the environment they are going to be flying in), hold a valid type rating (as the Learjets are individual types and not covered by a class rating) and hold an IR (as they will probably end up IFR and need controlling at some point). And this answer is assuming that I had lobster for lunch, followed by a nice cappucino with chocolate sprinkles and a great shag last night.
So, to do all this, you would have to take the ATPL exams, have to do an initial IR and then complete a course of training, and then take a Licence Proficiency Test on type with an IR included (for which you would have to have enough experience and ability to pass which means you would have no problem with the professional GFTs). If you think about it, is what you have to do to get an ATPL in the first place - and which probably explains why no-one has done it.
Theoretically possible, but there's no point.