What should I do to atone for my sin after lying to a traffic police officer so he wouldn't issue me a ticket?

Swearing by Allah falsely is forbidden and a major sin, considered one of the greatest sins. It is called "al-Yamin al-Ghamoos" (the plunging oath), which plunges its swearer into sin. The proof for this is the saying of the Prophet, peace and blessings be upon him: "The major sins are: associating partners with Allah, disobedience to parents, killing a soul, and al-Yamin al-Ghamoos." Repentance to Allah is obligatory, along with the firm resolve not to repeat it. Many scholars believe that it has no expiation because it is too great to be expiated.