if he wanted eowyn she would have despised him. if he wanted gold he'd have no where to spend it. if he wanted power he was never going to get it with saurman. I never understood what drove his character.
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Grima had power as Saruman's agent who controlled the king. The White Wizard may well have made promises to Grima that he didn't necessarily intend to keep. He might have even promised that he could make Éowyn love Grima.
Saruman probably decived him with fantasies of power, wealth and whatever else he wanted.
I wouldn't feel too sorry for Wormtongue though; he was probably already prone to such a betrayal of trust.