Here is a good article on Covid vaccine effectiveness duration: https://www.abc.net.au/news/health/2021-02-16/covid-19-how-long-will-coronavirus-vaccines-last-australia/13130530

It is too early to tell how long the current released vaccines are effective, but I think your thinking only several months is not substantiated by the current information.

There is no "permanent vaccine" guaranteed to be coming in the future. There might be and the vaccines already released might even be one, just too early to tell. We can't speed up a test subject to see how long they last.

The current vaccines all reduce the severity of symptoms from Covid, i.e. no one who has received a vaccine has had to be hospitalized. So if that remains the case, then I think lockdowns would go away as if no one is dying then no need for a lockdown which is a pretty severe health measure. In my longish lifetime, I have never seen lockdowns for health reasons until now so pretty unusual.