Does lust increase as good deeds increase, and is there any basis for that in the Qur’an and Sunnah?

This statement is incorrect; rather, it is one of the apparent abominations of speech. The Holy Quran has indicated that righteous deeds curb the desires and prevent one from indecencies and evils. Islam came to regulate and refine desires, because their unrestrained release leads to the degradation of man and the corruption of society. Desire is a trial from Allah Almighty. Whoever controls it with the lawful restraints and places it in what is permissible will be rewarded, and whoever places it in what is forbidden will bear a burden of sin.