Likely not possible on iOS. Apple has too many restrictions. It works with lemmy because lemmy has a free API and doesn’t attempt to obscure it’s code. New reddit employs a ton of stuff to try and stop these types of efforts. Apple has a ton of restrictions surrounding code execution and browsers (all browsers have to use safari’s engine). That being said, I am not an iOS developer (outside of cross platform tooling), so it might be possible, but from what little I know of Apple’s policies, not likely.
That being said, I am thinking about the idea of a reddit proxy addon for lemmy, something that would expose r/* communities to lemmy via an API. This would primarily be of use for developers, but could potentially allow r/* communities to exist alongside lemmy communities, with the caveat that reddit users would not see comments. The proxy would actually scrape reddit for posts/comments, cache them in redis, and offer the cache up via a restful API, so it wouldn’t be realtime, but it would be a starting point.