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.

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

I read an article[1] a while ago where some people made a dashboard with all streams and data. Never tried it though. The application is called race control and is opensource [2]. If the app is not what you mean, their reverse engineered api client might help?

1. https://tweakers.net/reviews/8900/naar-diverse-f1-streams-te... (dutch)

2. https://github.com/robvdpol/RaceControl

You can extract the data by sniffing the app's traffic, but it's not easily done.

Live timing isn't that hard, live pseudo-telemetry like the app delivers is really hard.

Also you ain't getting it for free unless you're super lucky - not that kind of industry. Ergast has non-live data, however.