Some SPAA radar could lock air targets in third-person view, some have to manually use the commander or gunner sight to lock the target, is this a vehicle-specific stuff? I mean I can third-person lock aircraft in the M247 while I cannot do the same with the ZA-35, or they all could do it and I didn’t find the correct key to do it? I only has one keybind which is IRST target on.
I’m not a professional SPAA user,but from my friend’s experience I could say that it’s 50/50,sometimes it lock from third person,and sometimes only from gunner’s sight. At least on pantsir.
When your radar indicator shows this 
triangle with retangle around it , it’s almost 100% you can lock them through the third person, Pantsir, Gepards, M247, Shilkas can do it, some just couldn’t, makes me wonder is this is a built-in feature for certain SPAAs.
Probably
It only works with SPAA that have a search radar. This is the turning thing ontop of most SPAAs
Not really, it has to have a search radar yes but not all search radars can do it. it’s more of a function of if the search radar and track radar can be slewed. Some vehicles even have a searching radar but uses IRST to track so slewing in that case might not be possible (on some vehicles IRL it is, and there are reports/discussions on the ADATS for example being able to do this IRL but not in game).
To answer OP’s question:
Yes, its a vehicle specific functionality but there is also a component of accuracy of the slewing and differences in line of sight of the tracking and searching radars that affect the chancers of acquiring a lock at first try. The ItO 90M is a prime example of this against helis as the search radar is so much higher up than the tracking radar so trees, houses and hills might hinder line of sight of one but not the other.
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I remembered some more info.
If there are the two lines beside the triangle in third view that means you have selected that target to try to lock if that key is pressed, but those lines also only ever appears if that target is within tracking range, so the ItO 90M for example can search out to ~20km range but the tracking radar can only reach ~16km.
You can see the ranges for radars in x-ray view in the hangar.