The lebanese are considered arabs because most lebanese do have arab descent and speak arabic and Lebanon was under arab rule. According to the lebanese constitution Lebanon is an arab country.
I don't know about Somalia Djibouti and the Comoros because the people there have african origins and don't even speak arabic so I have no idea why they are in the arab league. Besides Comoros is geographically so far away from the arab countries...so I dunno.
In my country, there are about 500,000 Arabs who are considered as "Malays" under the Federal Constitution because all Muslims who habitually speak Malay Language are considered as "Malays". Most of Malaysian Arabs (about 80% of them) are originated from Hadhramawt region in Yemen, and 99% of them are no longer speaking in Arabic. The remaining are originated from Hejaz, Iraq and Egypt.
And most of Malaysian Malays have Arab ancestry, in fact many Malay scholars claiming that all Malaysian Malays have Yemeni ancestry...
Famous Malaysians of Arab descent
1) Sheikh Muszaphar Shukor Al Masrie (Egyptian origin) - astronaut and surgeon.
2) Datuk Shake (Yemeni origin) - singer
3) Azalina Othman (Yemeni origin) - minister of youth and sports
4) Ning Baizura (Yemeni origin) - singer, actress
5) Syed Sheh Hassan Barakbah (Yemeni origin) - Governor of Penang
6) Syed Sheh Abdullah Shahabudin (Yemeni origin) - Governor of Penang
7) Sharifah Rodziah Barakbah (Yemeni origin) - 1st First Lady of Malaysia
8) Zara Salim Davidson (Yemeni origin) - wife of Perak's Crown Prince
9) Sharifah Amani Al Yahya (Yemeni origin) - actress
10) Tuanku Syed Sirajuddin Jamalullail (Yemeni origin) - King of Perlis
11) Tuanku Syed Putra Jamalullail (Yemeni origin) - King of Perlis
12) Tuanku Syed Mahmud Jamalullail (Yemeni origin) - King of Perlis
13) Tuanku Syed Hamzah Alwi Jamalullail (Yemeni origin) - King of Perlis
14) Tuanku Syed Hamzah Jamalullail (Yemeni origin) - King of Perlis
15) Syed Adney Syed Hussein (Yemeni origin) - footballer
16) Syed Thajudeen (Yemeni origin) - painter
17) Munshi Abdullah (Yemeni origin) - author, translator
18) Syed Hussein Al-Attas (Yemeni origin) - politician
19) Syed Muhammad Naquib Al-Attas (Yemeni origin) - Historian
20) Syed Hamid Albar (Yemeni origin) - Home Minister
21) Syed Jaafar Albar (Yemeni origin) - politician
22) Syarif Masahor (Yemeni origin) - Fighter against British colonisation
23) Syed Mokhtar Al Bukhary (Yemeni origin) - Billionaire
24) Syed Nasir Ismail (Yemeni origin) - Speaker of Parliament
25) Joe Hasham (Lebanese origin) - actor
26) Betty Banafe (Yemeni origin) - actress, singer
27) Burhanuddin Helmi (Yemeni origin) - Islamist
28) Meor Abdul Rahman (Yemeni origin) - Martial artist
29) Nur Lydia Ibtisam (Egyptian origin) - Actress
30) Osman Aroff (Yemeni origin) - Chief Minister of Kedah
31) Syed Nahar Syed Sheh Shahabuddin (Yemeni origin) - Chief Minister of Kedah
32) Syed Razak Barakbah (Yemeni origin) - Chief Minister of Kedah
33) Radzi Sheikh Ahmad (Yemeni origin) - Home Minister
34) Sharifah Aini (Yemeni origin) - singer, actress
35) Sharifah Mazlina Syed Abdul Kadir (Yemeni origin) - first Asian woman crossing the Antarctic, lecturer
36) Sheikh Muhammad Tahir Jalaluddin (Hejazi origin) - Islamic scholar
37) Hamdan Sheikh Tahir (Hejazi origin) - Governor of Penang
38) Syed Ahmad Al Hadi (Yemeni origin) - Islamic scholar
39) SM Salim Al Mahros (Yemeni origin) - singer
40) Syed Abdullah Al Edrus (Yemeni origin) - author
41) Syed Ahmad Idid (Yemeni origin) - High Court Judge
42) Syed Azizi Syed Abdul Aziz (Yemeni origin) - anti-government blogger
43) Zeti Akhtar Aziz (Yemeni origin) - Governor of Malaysia's National Bank
44) Imad Al Khair (Lebanese singer) - nasheed singer, calligrapher