Both Mastodon and Lemmy (and Mbin) expose an API, which can be used to develop an alternative client (for e.g. mobile). This allows even for several alternative front-ends, like Elk, Phanpy and pl-fe for Mastodon (and Pleroma and Akkoma and some Misskey forks and several projects for single-user-instances - all of these extend Mastodon API in some way), or Photon, mlmym and Blorp for Lemmy. GoToSocial (made for single-user-instances) does not provide any webUI, pointing to these alternative front-ends. Lemdro.id even swapped its interface for Photon.
Technically one is able to develop a Fediverse instance software which would provide both Mastodon API (likely with extensions) and Lemmy API. With e.g. microblogging (and maybe events?) used via pl-fe and Threadiverse content more easily available via Photon or Blorp? But I am not aware of any project like that.
Corporate social networks generally don't like being mirrored by a competition and actively fight with these.
Bluesky was being mirrored like this by Bridgy, but as it is a two-way bridge and Mastodon users did not expect their data leak to another network they bullyed Bridgy dev into making it opt-in.
There are more issues to mass-mirroring content from outside and I hope others will tell about them.
Both Mastodon and Lemmy (and Mbin) expose an API, which can be used to develop an alternative client (for e.g. mobile). This allows even for several alternative front-ends, like Elk, Phanpy and pl-fe for Mastodon (and Pleroma and Akkoma and some Misskey forks and several projects for single-user-instances - all of these extend Mastodon API in some way), or Photon, mlmym and Blorp for Lemmy. GoToSocial (made for single-user-instances) does not provide any webUI, pointing to these alternative front-ends. Lemdro.id even swapped its interface for Photon.
Mastodon clients list (scroll down) and Lemmy clients list
Technically one is able to develop a Fediverse instance software which would provide both Mastodon API (likely with extensions) and Lemmy API. With e.g. microblogging (and maybe events?) used via pl-fe and Threadiverse content more easily available via Photon or Blorp? But I am not aware of any project like that.