Avoiding details for spoilers so just asking generalized question - if Boston Airport settlement is lost due to quest choices, is there way to retake it?

Have tried the direct approach, kill all brotherhood at airport location but that doesn't unlock the workbench again like at other settlements where kill all opponents = take control of settlement work bench.

Is the airport settlement lost for good? Anyone found way to re-tke it if losing it via faction choice?

Gone. But with no food options, it isn't really a "settlement" anyway.

I didn't have any people there and no real loss from a real estate pov. Agree lot better plots to build on. But I did build up quite a defense fort, and while it lasted - really nuked the heck out of the brotherhood next door.

Even though settlement status was lost, apparently the stuff I built there still 'belongs' to me and it fired on the Brotherhood after I went hostile to their faction. Problem is, with no settlement status / workbench access, I couldn't repair anything, so slowly my turrets all got shot up - mostly, actually a few still left operational but if the generator goes or no supplies, either way those defenses will eventually die.

Was hoping I could retake the settlement, just so I could rebuild my defenses.

You will eventually be able to reclaim it, just keep going through the main quest.