What is the ruling on dedicating supplication in Ramadan for whoever wins the lottery, and does this fall under the category of a good innovation (bid'ah hasanah)?

A Muslim's supplication for his brother in their absence is a righteous deed beneficial for both the supplicant and the one supplicated for, as the Prophet (peace and blessings be upon him) said: "Whoever supplicates for his brother in his absence, the angel assigned to him says: 'Amen, and to you the like of it.'" Supplication in absence (bi ẓahr al-ghayb) means supplicating for the one being prayed for secretly and sincerely, and the virtue extends to supplicating for a group or for Muslims in general. Some of the predecessors used to supplicate for their Muslim brother so that their supplication would be answered and they would receive the like of it. There is no basis for drawing lots in this matter; it is an innovation (bid'ah), and worship is based on divine command. Therefore, one should supplicate for the entire group. The "good innovation" (bid'ah ḥasanah) refers to a linguistic innovation, not a religious one. An example is the saying of Umar (may Allah be pleased with him) regarding the standing prayers of Ramadan: "What a good innovation this is," because it was not performed in this manner before, but it has origins in the Sharia.