Compulsory car insurance is required by law in Lebanon. It covers bodily injuries or death due to an accident and excludes any material damages.
So the question remains - Third-party or all risk car insurance?
Deciding this may depend on various factors like car specifications, vehicle history etc. What you should know while deciding is, third-party car insurance covers the policyholder against financial or legal liabilities arising due to injury sustained by a third-party or damage to a third-party’s property or car in a car accident. 
All risk car insurance covers own damage as well as Third-parties. Depending on any add-ons you choose, It may also cover damages arising from certain situations like total loss, theft, partial loss, vandalism, accident, fire, natural calamity etc.
Depending on your vehicle and budget, you may opt for a combination of third-party or all risk car insurance along with compulsory car insurance.