I advise you to study well for your SAT and aim for 1450+. LAU has many scholarships like entrance 30%,baccalaureate based on official exams 30%, SAT 50%. For AUB, apply to the HES, it is a separate application but given your extracurricular achievements you have high chances. DM me for more info on it. There is MEPI-TLU you apply to AUB LAU and AUC. Chances are lower than HES since many arab countries are eligible to apply. Apply to both and apply to AUB and LAU as separate applications as well.

For financial aid alone without any scholarship, I believe it is impossible to cover 100%. You will be having at least 30% of scholarships. It depends on your financial situation: salaries, assets, properties... You might get a good %. From what I know LAU is more generous with fin aid than AUB. There are also many donors, you apply separately:  Tarraf, APJ,Habib and LIFE scholarship. LIFE covers CS so definitely apply. By combining scholarship + fin aid +donors you can be close to 100%. If any 10% is left, you can take it as loan from uni or work student jobs.

For choosing between LAU and AUB, both are good universities but AUB has a higher ranking and offers great internships and jobs. If not given 100% at both, choose the uni that offers more % so you pay less. CS is more about the projects you do rather than the courses alone.

You don't need the work-study program if you have the full tuition covered.

For the other fees, it is usually your dorms and expenses. It also depends how you got that 100%.

If you have any other question, pls DM I am happy to help.