Lemmy will never really grow beyond what it is now. Even if there was another influx of users, the retention rate is going to be low and the amount of active users is going to be even lower. It will forever remain a niche platform for 3 reasons:
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It's made by and for people on the far left, tech/privacy nerds, and people who have been kicked out of Reddit. Because of this, the actual active users on here tend to fall into of these 3 groups, and they define Lemmy's culture, and this includes the developers. Because of this, much of content on here revolve around niche topics and so there isn't much here to appeal to the mainstream.
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It is fundamentally flawed by design. There are bunch of different communities on different instances about the same topic, and there is no way to consolidate them. Because of this, you have a bunch of dead communities that operate as independent nodes, instead of having centralized communities that are big and active. This issue would've been solved if Lemmy was designed to have each instance be a community in of itself (AskLemmy has its own instance and so does tech, gaming, and so on), but instead we have the current implementation.
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Lemmy has many of the problems that drive people away from Reddit. Sure, Lemmy isn't a greedy corporation, which is nice, but it still has terminally online powermods with little to no accountability, a hostile and negative community, weird/extreme echo chambers that make most people cringe, and so on. If you sign up for Lemmy, you're going to get the same problems but with a worse experience because it's way smaller and has less content, so why would you come to Lemmy instead of making another Reddit account?
I just don't see Lemmy every becoming mainstream or overtaking Reddit. It's already been 6 years since the start of Lemmy's development, and 2 years since the big influx of users from Reddit's API fiasco, and it STILL has to rely on the same dozen or so people spamming the platform to keep it barely active. Lemmy won't collapse, but it also won't be more than what it is now, at least not any time soon.