Try recording a video with sound on bluetooth speakers with as much fps as possible, then also record a second video with regular speakers, then cut+reencode(avidemux is an option) the videos so they start at the same video frame and compare their audio wave (audacity with ffmpeg support is an option).
If you don't have a video recorder you could use a screen recorder solution (like obs) with a microphone, but this would add more variables so it might reduce accuracy.
The precision of the measurement will depend on your test video fps, recording device fps and screen refresh rate.
I believe it is possible that the lag varies because of bluetooth interference and/or hardware implementation specifics, you might need to do several tests to know this for sure.
Listen , stopwatch and lipread - don’t know of any software solution... – Solar Mike – 2018-01-08T21:27:26.260
I already can guess it using MPC (playing with +/- keys to adjust audio delay). I need a more accurate way. – laggingreflex – 2018-01-09T22:02:11.867
There should be a fairly simple app for making the guessing a bit more accurate. The app makes a sound and asks you to click when you hear it and then shows you the time it took, maybe average a couple of tries. – laggingreflex – 2019-07-06T23:39:21.357