Is there a specific mantra to recite while lighting a lamp for Deep Daan?

Yes. The traditional Deepak Mantra is: ‘Bhoo bhuva suvaha, deepo jyoti parabrahma, deepo jyotir janardhana, deepo harastu papam mama jyotir namostute.’ This mantra identifies the lamp with the supreme light of Brahman, invokes Vishnu (Janardhana), and requests the lamp to destroy the devotee’s sins. It should be recited before lighting, while holding the unlit lamp in both hands.