I've been working on a bot, and when things are working it synchronizes almost instantaneously, including edits to posts and new comments. Any significant delay should be rare.
There are a bunch of reasons why things might be out of synch - load issues, software compatibility (lemmy.world is still on 0.17.4 while lemmy.ml has upgraded to 0.18), bugs... It helps to keep in mind that Lemmy is barely more than beta at this point.