Why does my Lily not show any intrnstiy minutes for two or more weeks although I do workouts and hiking etc...? My heart rate ist detected correctly, but the intensity minutes do wlways show as zero.... Please help me!

Please post a screenshot of the daily HR graph from one of such days, where you did some intensive workouts without getting any intensity minutes. 

The HR data indeed shows that the Intensity Minutes should have been awarded. Either the IM data was not synced (for example due to a crash and reboot of the watch), or there is a problem with the watch / Garmin Connect account association.

First of all, I'd try to sync over the USB cable to a computer with Garmin Express - sometimes data that did not sync over air, can still be synced in this way.

If it does not help, then there is little chance to recover the missing data, but you can try some steps to avoid that the problem continues:

1. Soft-reset the watch. Not sure how it is done on the Lily, but on most watches you can reset the watch by holding the Light button for some 20s till it shuts down, then waiting a few secs, and restarting. In doubts check the user manual, and search for the reset instructions. This reset will not erase any data. Master Reset would do it, but for the moment I would not recommend the master reset.
   
   
2. Look at the hint #4 in the Troubleshooting guide for (some) data missing after syncing, and follow the instructions there. This should re-align the watch with your GC account.

Hello again,

Thank you very much for your support.

I have good news- the soft- reset worked! I tried and now the intensity minutes show up correctly :-)

At the other hand, garmin express didn't find my watch, I connected it with the USB several times but the connection failed somehow... but that. doesn't matter in the moment.

Best regards, Gabriele