[kalal]

If you subscribe to F1TV you get timing data in form of additional screen which you can view. Apart of that, there were several attempts in the past to extract timing data from from live streams, which stopped around 2016 when the API was changes. So to my knowledge, there is no free API for that. If there was payed version, I would be also interested, but I don't know about it either. The thing is that F1 considers this traditionally very sensitive information and is unlikely to make it public any time soon.

[pedrovhb]

Perhaps a kind soul could implement an OCR system to extract data from the timing screen and make that available via an unofficial API :)