HL7 is the industry standard for medical data.
However you’ll have to write an HL7 interface and then become a HIPAA covered entity under your physicians or be a covered provider to legally receive electronic medical records.
Now if your physician has a Patient health record system or sometime referred to as a patient medical record system PHR/PMR Connected to their electronic health record EHR/EMR system they can release records to the PHR. In which you could create an account in and view your results if the provider does that.
Under HIPAA you are entiled to copies of your medical records with some restrictions, and you can request that from your provider a electronic copy of your record within 48 hours of the request. all EHR systems that are HIPAA complient have to provide this feature. However most cases the records are exclusively sent to a PHR and your account in that system.
Please note you do not own your medical records and things like physicians notes and impressions do not have to be released to you. Other types of records not released typically are psychological records or substance abuse records as that they are mostly subjective observations and impressions style notes and documents.
Are you looking to enter the EHR/PHR market? If so you’re about 15 years late and will have tons of competition in and overly saturated market. Now I’m not saying don’t try, but you’ll have a steep learning curve to climb and tons of laws and regulations you’ll have comply to. As well as tons of other standards like loinc, XDS-b, X11, etc... you’ll have to be experts in to even receive and then decipher the electronic medical records.
Now for the answer to your question; no there are not normally consumer/public API’s available to access lab results for the average off the street developer.