As others have pointed out the clear option is PeerTube. The fascinating thing about PeerTube right now is that the frontend experience actually seems to be best on other services. This is primarily because discoverability between instances is fairly poor due to both federation mechanics and due to the nature of bootstrapping social. Because Lemmy and Mastodon feature their own human driven mechanisms for content discovery this problem is largely solved so long as you are browsing through another platform (the same mechanisms do not seem to transfer well to a youtube like frontend, although nobody has tried yet). Comments made on Lemmy and Mastodon will also federate back to PeerTube so you're not segregated based on what service you follow from.

You can subscribe to channels from both Lemmy and Mastodon. Check out some popular channels:
!veronicaexplains_channel@tilvids.com
!letstalkphilosophy_channel@tilvids.com
!alliterative_channel@tilvids.com
!kde@tube.kockatoo.org
!lofiorchestra@makertube.net
!random_retro@makertube.net

NOTES:

• All of the above are channels. On Lemmy you can only subscribe to channels while on Mastodon you can subscribe to both channels and users. This is important as some videos get federated under the channels and some under the users. I believe this is up to the individual creator.
• Whitelist only is still fairly popular among PeerTube instances so you may not be able to access all creators from your Lemmy instance.
• Federation does not backfill so if the channels appear blank don't panic. It will fill in with future videos.
• If you follow these channels from Mastodon and then put them in a list you have a feed that is analogous to Youtube's subscribed page