You can obtain a Police Clearance by two ways:
Give a Power of Attorney to a person residing in Lebanon.
Apply for the document through the Consulate Office in providing the following:
A letter signed by the applicant.
Identity Card (for the Lebanese and Foreign Citizens)
A photocopy of the Passport first page and all the pages stamped by the Lebanese Authorities (for Foreign Citizens)
This formality is free of charge and may take up to four months to be obtained from Lebanon.