In Brazil we had a social media site that was huge during the 2000s called Orkut, it was owned by Google. It was sort of a mix between Reddit and Facebook: you had your own profile with pictures but you could also join communities that were organized in a searchable manner, like Reddit. Several of those communities migrated to Facebook, but they lost A LOT because Facebook wasn't meant to be used in this way.
I think the same thing will happen with Reddit. It will be more like 9gag and less like Reddit. Communities like r/funny or r/whatcouldgowrong will prosper while communities like r/askhistory will move forward crippled.
I don't think Lemmy will get a relevant share of Reddit (on Reddit's perspective) users. It has already obtained a relevant amount of Reddit users (on Lemmy's perspective) and it should keep being pushed for Reddit orphans, but it will be smaller and communities here shouldn't be as restrictive as they would be on Reddit. Instead of making c/dogs, make c/pets and include dog owners, bird owners, fish owners, else you will exclude people and have a dead community.