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

No — Baron Nashor enters exhausted. Units enter the board exhausted by default (Rule 143.4), and Baron has no Accelerate and no "enters ready" text; his ability only changes where he enters — the Baron Pit token replaces the destination you chose, and the Pit then becomes contested and stages a Non-Combat Showdown.

Controlling both battlefields doesn't change that, because control only matters for where you're allowed to play him (a battlefield you control, or your base) — it doesn't grant ready.

One gap: I can't pull a Riven Legend from my card database (only Riven, Shattered / Riven, Broken Blade / Riven, Deserter units and Blade of the Exile), so if the legend is what you're expecting to ready him I can't verify a ready clause. If it's a "when you play a unit to a battlefield you control" trigger, that condition is met on the play, but Baron's replacement sends him to the Pit — whether the ready follows him there depends on the exact printed wording, so I'd need the legend's text to pin that down.