My reading of "No justice, no peace" is not "If there is no justice, then will not allow peace", but rather "Without justice, peace is not possible"
This is the far more sensible reading imo. A free, peaceful societies must rely upon universal, and equal enforcement of law in order to encourage and protect peaceful behavior.
That's not to say that there aren't other ways to attain a "peaceful" society. Totalitarian regimes may have little to fear from their citizens, but only through the extermination of dissent and corruption. But, that's where the "free" part is important.
I'm not talking about a 'reading' of "no justice, no peace" in written, analytical form.
I'm talking about it chanted by a large group on the move with a grievance. Context, volume, and tone matter.
The chant is occasionally extended to "no justice, no peace, fuck the police" [1] and the phrase is celebrated even without that extension for its association with "fighting back" [2]. The phrase is also used euphemistically to predict riots are due [3].
In the protest-chant context, everyone knows it has two meanings -- both the cryptic threat, and the more cerebral koan -- at the same time. Indeed, that's part of its charm -- people who aren't quite ready to throw rocks and break things can chant emphatically along with those who are ready, and get a little vicarious thrill that some serious shit might go down... "even though we didn't really mean things to get out of hand".
There's also the group-chant version: "No justice, no peace". In that form, it's almost a threat: agree with us or we'll riot.