If I am at NAIA 3, and I want to get on the closest bus to Lucena... Are there companies going to Lucena from Pasay? or do I have to go to Buendia LRT bus stations?

Albert,
The Jam and Jac liner terminals at Buendia are in Pasay
The alternative is to hail an Alabang bound bus on Edsa then change at South Station to a Lucena bound bus
These will be local buses,most without air con
The Buendia/LRT location will offer you a choice of Jam or Jac liner(with on board wifi) from an air con terminal.
The extra time and cost to get there rather than Edsa/Pasay( which I think is the basis of your question) is minimal and if you have luggage will be much easier.
I think the longest wait for a service in one of the two terminal would be 20 minutes or so during peak times

Ok, then.
So I will take the 20 php bus Shuttle from NAIA 3, that leaves me at Taft MRT, and then get a jeepney to Jac Liner terminal in Buendia... My luggage is just hand carry.
How does it sound?

Sounds fine. You could try your luck at riding the two stops to Buendia from Edsa.
If you are travelling off peak and have only hand luggage you may be allowed on LRT.
Really depends on how strict the guard is and how big your hand carry is
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