So Lando is within range one of another ship with a lower pilot skill. Lando makes a green maneuver and gives an evade to the other ship. Can the other ship then take an evade action during its own activation?

Nope, Lando doesn't give away the free evade. He lets the other ship perform a free action. So that would require the target ship to perform the evade action twice.

It can't do the same action twice even though the free action wouldn't be performed during its own activation? I would think the whole "can only perform one action an activation" thing would be bypassed...

It can do an action in its own activation phase after getting an evade action from lando, it just can't do the evade action again. You can't do the same action twice in one round. Evade and focus, fine. Evade and target lock, fine. Evade and evade again.... No.

Well, Poodoo.

Thanks for the answer! Even if it wasn't what I wanted to hear.

Core Rulebook, Page 9:

However, a ship cannot perform the same action more than once during a single game round (not even when the action is a “free action”).

So Lando is within range one of another ship with a lower pilot skill. Lando makes a green maneuver and gives an evade to the other ship.

Lower PS activates before higher PS. So the other ship (with lower PS) activated before Lando.

Can the other ship then take an evade action during its own activation?

No, because it will not activate again this activation phase.

And because of the reason mentioned above by others.

And just a side note, being assigned tokens does not constitute an action.

So if Lando had Jan Ors on board flying with an E-wing, you could:

E-wing: move + evade action

Lando: move + give e-wing a free action

E-wing: takes a focus free action from Lando

Jan: assigns evade token instead of the e-wing's focus action

Then the e-wing is left with 2 evade tokens.

You could gamble with Lando Crew. Take Han or Chewie on a YT1300 with the falcon title and Lando crew. Then use Experimental Interface or PTL to take an Evade Action, then a Lando Action or a Lando Action then an Evade Action. Lando is a gamble, but he's capable of getting you 3 evades for 3 total evades. Sometimes Lando will blank and get you nothing, but usually he will get you at least a focus or an evade token.