lactate threshold based heart rate zones

Yes but be prepared erratic heart rate recordings from the wrist that might affect the automatic settings. For stability use the strap. 

to tell the truth I was comparing the strap and the watch HR for a while, and they mostly match. Unfortunately there are 2 cases when they don't:

1. when I do short, fast intervals, the watch doesn't get to the real HR, the strap does. This is a known issue.

2. the strap sometimes has readings that look... well let's call it "random". It's not related to what I do or feel. The watch does good in these times.

So for knowing my HR I trust the watch more than the HRM :( When I do intervals I know it's higher than what the watch displays. But when I run for longer time with a relatively stable pace (training or even a race) I think I can trust the watch.

I'll try to wear the strap when I do intervals. This way I (and the Garmin algorithms) will have a chance to see my higher HR.

You can use build in HR sensor for walk, resting or other very calm activities.
Regarding 1. it is not an issue, it is how your body works, there will be always a delay with pulse change on your wirst and sensor located there will never work correctly for intervals.
Regading 2. I cannot tell you why you have such issue, for me chest readings looks stable.

When I compare wrist readings and chest readings, ususaly my hart rate recorded on wrist is 10 to 15 beats lower than on the chest, what of course completelly changes all data and estimations.

To be fair not even the strap will record the max heart rate reached during a short sprint; there’s a lag at both the start and the stop of the sprint but it is better than the OHR. 
if you’re getting ‘random ‘ results from the strap check the fit and ensure it is well wetted before starting. I soak mine in warm water.

In general I believe Garmin has made huge progress with OHR and often don’t use a strap too but if I want certainty in the reading then it’s the strap that I turn too.