Looking at the case rates in the UK, you can see they are very very low in population cohorts that are 90% vaccinated or more. It seems likely that breakthrough infections of delta would still control infections, without lockdown,
Probably. As I understand the latest reports, and in particular the Provincetown, MA breakthrough cases (https://www.nytimes.com/2021/0…rovincetown-cape-cod.html), the existing vaccines can control Delta. They can even eliminate it, once ~85% of the population is vaccinated. However, this can only be done by continuing to use masks and social distancing for about a month. First, vaccinate ~85%, then wear masks for a month to prevent breakthrough cases. By that time, the number of infected, contagious people will fall to zero, or close to zero. Any remaining cases should be trackable. The patients can be quarantined. If there were a few hundred per day in country such as the UK, Japan or the US, the cost of tracking would be negligible.
A booster shot targeted to Delta would be better, but it is not essential. That's what I think the reports say.
Provincetown came as a shock to the CDC. However, people should keep it in perspective. On July 4, there were 30,000 people in the town, 75% of them fully vaccinated. Mostly young people carousing, jamming bars and house parties, and "making out." There were 965 cases, many of them breakthrough, but only 7 hospitalizations and no deaths. In Provincetown itself they have gone back to using masks and social distancing. That is a very liberal, Democratic part of the country where just about everyone is vaccinated and will do what the doctors recommend. (I know the place. I was there a few years ago when my daughter was working at the National Park nearby, as a naturalist.)
On the internet I have already seen several people claim that 965 breakthrough cases in Provincetown prove that "the vaccines do not work" because more vaccinated people got sick than unvaccinated people. People who say that do not understand statistics. Heck, they do not understand simple arithmetic. There are no unvaccinated people in Provincetown! (Okay, practically none.) If every single unvaccinated person there got sick, they would probably still be outnumbered by the breakthrough cases.