Automated syncing of medical records and blood labs is not supported.
The key blood levels can be easily added manually, however. This allows not only the fancy Apple Health syncing blood labs, but literally any other type of blood test whether it is a PDF or a printed sheet of paper.
The supported measurements are the ones that are most actionable for longevity, especially cholesterol levels and LDL/HDL breakdowns.
If you are trying to track your cholesterol or other lab values you can enter those directly into the vault at https://gyrosco.pe/vault/ or from the blood levels screen in the app. Since these are only measured a few times a year, at most, this should only take a few additional seconds and isn't much extra work.
We don't provide analysis of that information, but adding it will let you keep it in one place and allow it to be shown in the trends view alongside your other metrics, seeing how things like your weight, activity, etc. affect these long-term metrics.