geddit isn't a client, it's an instance/server of Lemmy (which has its own API). To say Lemmy doesn't have an API is false. It very much does. (In order for there to be apps for Lemmy, it would logically follow that there's an API for them to use.)
I am not a fan of a reddit relay (at least, not on here). We should be building a new community here rather than amplifying posts from the other place. Of course, you are free to set up your own instance that does this but I won't be supporting that here.
I'd like to know how you'd propose to set up something like that, considering reddit API access is unreasonably expensive (which prompted the exodus away from reddit in the first place). Because you need a way to talk to reddit too. That's what APIs do ("application programming interface" - it's in the name). In my understanding, you can't just code something like that without a) accessing reddit's API to read posts and b) accessing lemmy's API to write them. Feel free to correct me if I'm wrong, though. They're not going to let you scrape their data for free.
But if you have a secret gold mine stashed away somewhere that you can afford this, why not contribute to the continuing development of lemmy or this instance instead of spending it on reddit's API access? You know, it's just a thought.