Could using coconut oil for an intimate lubricate cause a uti?

Possibly: Use a lubricant designed for that specific purpose, not something not intended to be used inside the vagina.

Coconut oil: Not likely that coconut oil would cause UTI . Uti is common in some women post vigorous intercourse, sometimes called "honeymoon cystitis". Ok to try other lubercant e.g. Ky jelley. Also if you do get UTI try drinking a lot of cranberry juice. You may need medication from your doctor.