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As far as I know Samsung matrix is better than LG for MacBook Air. There are two kind of Samsung matrix available - LTH133BT01 and LSN133BT01. Which is the best?
Unlike the older MacBook & MacBook Pro series the MacBook Air display is ultra thin which is why its display is not as good. To add to this each display has a code which the system leverages to ID its dimensions and scan rate. I haven’t tried substituting displays in the Air series so I can’t tell you if a thicker display will work and the limitations of the lid may prevent it from closing. Given the risks and the expense it might make sense just getting a newer MacBook Air as Apple has improved the screen used in it quite a lot!