What do you do when you experience lustful thoughts while reciting Dhikr, seeking forgiveness (Istighfar), or reading the Qur’an? Do you continue with the recitation and seeking forgiveness?

There is no confirmed reason for what you mentioned, but reciting the Quran and seeking forgiveness (Istighfar) should not be abandoned, as they bring peace to the heart, expel the devil, and heal the servant. Allah the Almighty said: "Those who believe, and whose hearts find satisfaction in the remembrance of Allah: for without doubt in the remembrance of Allah do hearts find satisfaction." (Ar-Ra'd: 28), and He said: "And We send down from the Quran that which is a healing and a mercy to those who believe." (Al-Isra: 82). Therefore, be diligent in seeking forgiveness, recitation, and remembrance (Dhikr) always, and stay away from evil thoughts and sense the greatness of Allah.