You won't see it on Lemmy because there is no way to follow individual users on Lemmy. Here's an example of viewing a Threads user from my instance. There is no content because Kara cannot interact with Lemmy and Lemmy users can't follow her.
On Mastodon, Threads accounts (or any account) won’t federate to your instance until you (or someone on your instance) specifically requests to follow. It’s a common misunderstanding when people think that federating with Threads.net will “overwhelm” a small instance.
Also, not every Threads account has opted into federation. So there's really very little available content out there.
Threads users cannot subscribe or post to Lemmy communities or follow Mastodon users (yet). Threads has a sort of halfway federation situation. Mastodon users can follow Threads users without having a Threads.net account but that's it.
Also, the ability to allow Mastodon users to follow Threads accounts is opt-in, and only a small portion of users have chosen to do so.