Have a job, but might not finish Ph.D. on time.
If this were a full-time tenure-track position, the answer would likely be different, because in many fields (particularly STEM fields) you'd probably be able to request a "gap year" that you could use to finish up your work and do a short postdoc stint somewhere before beginning your full-time position.

However, as a lecturer or instructor, you don't have nearly enough leverage. You may ask if it's possible to start the position if, for instance, the thesis has been submitted but not defended by your planned start date. But I would get in touch with them as quickly as possible and ask what would be the latest you could get your degree before starting. Then, if you feel you can't make that deadline, try to negotiate (but be aware that it might not work!).