The reason for those particular three lions though is very particular to a Plantagenet ruled England.Basically I agree with claim, but we also should have in mind that three lions is the best known CoA of England and, to be honest, lions is just popular heraldry figure. I can imagine that such heraldry symbol could appear not for the normans, but just for another feodal.
The best option, as for me, set dragon as CoA pre-norman period and give for any ruler (or at least non-anglosaxon ruler) of England design to change the CoA on three lions.
P. S. And, of course, I would be glad if the same option will appear for Rus too.
An England that hadn't held Aquitaine could well have stuck to just the two Lions it had had passed down via the connection with Normandy, rather than combining the two Norman and one Aquitainian lion into the Plantagenet associated coat of arms. Conversely an independent double duke of Normandy and Aquitaine could equally well have united the two in the same way. It isn't really right for a Norman conquest era England either.
Without it, we could well have seen a very, very different setup, maybe retaining the single Lion Rampant as used by Henry II, or the counter rampant lions as apparently used by RIchard I.
And yes, I know it's the iconic "real world" English arms, but we spent more time under France quartered with England than we did with England alone. We only dropped the French/English quartering in 1707, and only eliminated France from the arms in 1801.