If my instance closes down, will I lose control over all of the copied content from my previous account
Once the old instance is gone, yes. If it fails suddenly and never comes back up, there's not much that can be done about that, unfortunately.
If the old server closes up shop in a planned way, and the admins give you enough advance notice, you can take whatever steps you want before the shutdown.
I'm not sure if Lemmy has this feature, but some servers (Mastodon, off the top of my head) have a "self-destruct" mode to send out delete notices during a planned shutdown. It's not a 100% guarantee that all the other copies will go away, but neither is deleting a random post from an active server!