Lucentio is a rich kid who travels to Padua to top off his education and "see the world." His plans to study and make his family proud are quickly abandoned when he spots Bianca and falls in love with her obedience to her father and her silence. Soon he forgets all about his studies and begins to gush about his burning passion for Bianca. He basically transforms into a giant cliché:
Tranio, I burn, I pine, I perish, Tranio,
If I achieve not this young modest girl. (1.1.156-157)
Hmm…this probably sounds a little familiar to anyone who ever felt like they would just "die" if they couldn't go out with the person they admired from across the school cafeteria.
We gain a little bit of respect for Lucentio when he tones down the whole "I'll just die without her" bit. Lucentio appears to be very crafty as he disguises himself as a tutor ("Cambio") and gets into Baptista's house where he has access to Bianca. Bianca and Lucentio eventually fall in love and elope. Game over. Lucentio wins, right? Not so fast. Bianca turns out to be a "shrew" and Lucentio has absolutely no control over his beautiful, young bride. This costs him his street cred with the fellas and a good chunk of change (he loses the bet about whose wife is the most obedient at the play's end).