I couldnt find any info on this.

You can use lions gate to remove power and give a trait to any character in play, correct?

Its not a cost to be played on your own characters only?

The cost to trigger its ability is to kneel it. A cost is always the X in any "Do X to do Y" construction. You are kneeling the Lion's Gate to discard a power from ANY non-house card in play, it can be yours or an opponent's. A cost can only be paid with cards you control (in this case your Lion's Gate), the actual effect can hit any target within the effects own restrictions.

Note that the "then" part of the effect can only take place after a power is successfully discarded from that card. So you cannot give a card a trait that didn't have any power on it.