That feature doesn't yet exist in Lemmy, though there are discussions about that on GirHub, so it'll probably be implemented eventually.
There is technically a way to transfer all your data from one instance to another if you have access to the database. For example, you take a database dump of your user and all your info (as mydata.sql) and ask the admins of the other instance to run that against their database, you'll be able to preserve all your user data that way. However, you're unlikely to get an admin to agree to that (since there's obviously a risk the SQL commands are malicious or you tampered with it in some way).