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The higher the parameter of sexual openness, the closer the girl is to the most ancient profession. And the less respect she has as a professional in the field of magic and alchemy.

If by lust you mean the pink stat next to your tiredness, then yes. If it hits max, Celica will orgasm, and be stunned for some number of her next turns. 

If you mean the stat that goes up each time you orgasm, then no, not really. As far as I know, at least. All it does is make Celica not cover up as much anymore when stripped nude. And later in the game, there's a way to lower it back down, so even if there is a downside in a later section, it can be reversed.