Can your Sims live on the same lot as their clinic?
Your Sim will have to buy a home lot first, then a lot for the clinic. But basically, yes, your Sim can have the clinic and the comforts of home on the same lot. Just be aware that if your Sim has a job, he or she will return to the home lot after work. Also if you click on the "home" button on your Sim's thumbnail, your Sim will go to the home lot instead of the clinic.
It works the same as with retail lots and restaurants if you've played those.