For the most part, Threads content just wouldn't appear on Lemmy at all. It's like how you can't see Mastodon users' timelines on Lemmy. e.g. Jeri Ryan from Star Trek is on mastodon.world, but you can't read her blog from Lemmy because it just doesn't display microblog content, only stuff that's sorted into groups (communities).
The one exception is that Jeri Ryan can track down the equivalent group on her Mastodon instance and "microblog" directly into the group. Mastodon has some hacky tweaks to do things like reading the first sentence as a heading, the second line as a URL, and the third line as the post body, so if you're especially dedicated you can post to Lemmy from Mastodon. If Threads cares enough, they could add similar functionality to Threads to make it technically possible to post to Lemmy as long as you try hard enough, but just regular people's blog posts on Threads won't display on Lemmy at all.