lost images after a migration, can I just load them from the wayback machine?

Download them from there and re-upload to your own server, yes. Don't hotlink them from archive.org though, it's slow and you're relying on someone else's server staying up. Before that, check the old host for a backup, a lot of them keep one for a while after you cancel. Wayback often only saved some of the image sizes, and sometimes not the full resolution one.