When i play a dockside Dockside Lock-Up and use the jarvan trigger to move nidalee in - do i initiate a combat showdown to draw with Nidalee, Cat Form

It depends on whether enemy units are still there after Dockside's own trigger resolves — with a lone enemy unit there, no combat happens and Nidalee doesn't draw.

You never "initiate" a Combat Showdown; it's staged automatically in a Cleanup, and only once the Chain is empty (Rule 462). Both Dockside Lock-Up's play trigger ("banish a unit here") and Jarvan's move trigger fire off the same event and sit on the Chain together, so both resolve before any combat can open — you choose the order (Rule 383.3.d), but that doesn't save it. With one enemy unit there, it gets banished as the Chain resolves, Nidalee then arrives at a battlefield you don't control with no enemy units present, so you get a Non-Combat Showdown and a Conquer — no combat, no "win a combat," no draw.

If a second enemy unit is still there after the banish, Nidalee arrives with defenders present, Combat is staged, she's the Attacker (she applied Contested) and she draws only if she remains after combat — if she trades and dies, no draw (she isn't present to evaluate the win condition).