I have riven legend. I control both battlefields. when i play baron, does it enter ready?

No — on the card text I can retrieve, Baron Nashor enters exhausted. His ability is only a replacement effect on where he enters ("If you do, I enter there"), not on his state; per Core Rules 369.3, abilities that describe how a unit enters replace the default entry, but Baron's text says nothing about readying him. Units enter exhausted unless something explicitly grants ready (Accelerate, "I enter ready," "Your units enter ready"), so nothing in his own text changes that.

Two things I could not verify, and they matter here:

1. I could not pull your Riven Legend from the database at all — not by name, not by domain search (Calm/Chaos, Calm, Chaos) or by the Riven tag. Only Riven, Shattered / Riven, Broken Blade / Riven, Deserter (units) and Blade of the Exile came back. So if you're relying on the legend's own ability to grant ready (e.g. "when you play a unit to a battlefield you control…"), I can't confirm it from the loaded card text — please paste the legend's exact printed text.
2. Even if the legend has a "battlefield you control" condition, note that when the Baron Pit isn't already on the board, Baron's own ability rewrites his destination to the newly created Pit, which you don't control (same pattern as the Here to Help + Baron call, FAQ #12610). A "you control this battlefield" trigger generally won't see him there.

If the Pit already exists and you control it, that destination issue disappears — and the legend's wording becomes the deciding factor. This is my interpretation based on Rule 369.3 and the default exhausted-entry rule; no official FAQ exists for this specific interaction.