I remember Rishi being against further lockdowns in December 2021, so that part checks, but not sure necessary to prevent it. Most of the parliamentary party didn't want another one then either. Him saying this now is an attempt to take credit for one of very few unequivocal covid policy wins.
As for whether it would've been different had Omicron been more dangerous, I suspect not. I don't think the building blocks for another lockdown were still in place by December 2021. There was more awareness of the harms of lockdown and the way in which they disproportionately affected people who were already disadvantaged, thanks to the ICO forcing the government to release that information the same month. That was taking up more space than it had done previously.
It's also hard to see what the rationale would've been, how it could've been sold to a public who'd already had enough. The first lockdown was if anything public driven, because we didn't know what we were doing and it's what most of the rest of Europe did. Later on, buy in for the 2021 lockdown was inextricably linked to vaccines. The population as a whole were willing to curtail their activities while people got a chance to be vaccinated. None of that applies by late 2021. Partygate as a story was also happening by that point, and I don't think the Tories could've convincingly called for another lockdown once that was known about. Too much erosion of trust. There's no convincing narrative available.