When you are looking to the word "safe" or "safety" I think you need to feel safe yourself. It is true there are police precincts on the lower east side that do make it very "safe" and yet, you will know best if you go into the neighborhood/s/ on your own at different hours - day or night - and see how you feel. If you go with someone and walk around you will be more knowledgeable than if you take someone else's word for it.
Safety is really subjective.
The reports and stats on the area show Lower East Side to be quite good.