How should I collect data for an "identifier" rather than classifier?
It depends on the use you are giving. The $not.lion$ class should contain sufficient data of different things, but also should contain tigers, cats, african landscapes without lions, etc.

Your idea of 50-50 is good.

Add this: The weights $w$ could help you define where your model should focus: Lesser weights when there is something easily distinguishable from a lion like a computer, but larger weights when there is an african landscape.