Leo III was influenced by the judeo-islamic traditions (which were strong in his home city of Germanikeia in Asia minor) forbiding the drawings of God/saints etc.
If Leo III is eliminated before becoming emperor (or overthrown in his early reign) and replaced by someone who doesnt hold such views then its possible that iconoclasm would be delayed or even called off...
On the contrary, the old theory that Leo was influenced by Judaism and Islam now seems less probable than it did before. This is, after all, less than a century after the death of Mohammed, and Islam is not particularly strong anywhere outside Arabia. The distant governing classes of the Caliphate are Islamic, of course, but mass conversions of their subject populations are yet to begin.
As for an Eastern Emperor being influenced by Jewish traditions, the idea seems fanciful to say the least. It's probably just easiest to say that Leo III was influenced simply by long-standing anti-idolatry traditions, and that he seized upon these as a way of placating God when the Arabs return to the offensive in the 720s.
If Papacy remains in friendly terms with Constantinople i guess that Popes wouldnt support the Lombards as they did in OTL... However if Papacy and their friends in Ravenna feel threatened by Lombards i guess that they would have turned to Charles Martel and the Franks for help...
The Papacy will have to turn to the Lombards or Franks sooner or later, no matter how good the relations are (and they were never particularly good pre-Iconoclasm) with Constantinople. To paraphrase John the Almsgiver, the Emperor is far, far away, and he has more important things to worry about than the remote backwater that is northern Italy.
You have to remember that the military victories of Constantine V (718-775, reigned 741-775) against the Ummayad Caliphate allowed Iconoclasm to survive. His successes were seen as a blessing from God.
I'm aware of the successes of Constantine V, thank you

. The whole swinging back and forth between icons and iconoclasm in the eighth and ninth centuries was linked to military successes and failures. Indeed, I'd go so far as to state that had the Empire not started winning dramatically in the 860s, we'd have probably seen a return to some form of Iconoclasm.
Which historian are you quoting there, by the way? Norwich?
Would this be beneficial for the ERE? Rome was one more border province requesting help against foreign invaders. Good relations with the Pope didn't guarantee victories to the imperial troops.
In the short term it makes pretty much no difference- the aid given by Constantinople to the Exarch of Ravenna and the Papacy amounted to very, very little by 700. Long term, the impact could potentially be huge. Or it could amount to very little. In my view, it's just a matter of time before the Pope starts to start looking West instead of East.