Yes, Lebanese citizens should get an Oman visa before traveling. This rule has just a few exceptions. The Sultanate used to allow visitors from Lebanon to enter Oman without a visa for up to 14 days, however, the visa-free entrance has now been halted until further notice. By far the easiest and most convenient option to get a visa for the Sultanate is through the Oman e Visa site.

You can get your Oman visa by applying for it online through Oman IE Visa. 
1) Visit Oman IE Visa
2) Select your country
3) Choose the required visa type
4) Fill out the application form and upload the documents
5) Pay the visa fee
6) Track your visa status and download your visa. 

You can get more information on Oman visas for Lebanon on Oman IE Visa. 

Yes, you can apply for your Oman visa online through Oman IE Visa.