When the next battle step starts, you gain control of one of your opponent's neutral units in that arena. At the end of that arena's battle step, return that unit to your opponent.
Text erratum. For Lando's Influence to work, it must be played before the battle step you want it to work in.
You can't play Lando's influence for the first battle step because Lando's Influence does not specify playing it before the battle step in any arena. Thus, it only works during the General POP after battle has already started in the first arena.