Maybe you were not born at that time but Atari was already in bad condition when releasing the Lynx.
The Lynx had some weaknesses (battery autonomy, size) compared to the the GB the main problem was the games.
Atari was at that time far weaker than Nintendo and could never attract the most famous developers.
Most of the Lynx games are were from the beginning from Epyx and Atari (Ten Gen, Atari games) while Nintendo could count on numerous well known companies.
Despite the Epyx first games were amazing (Electrocop, Blue Lightning...) the Lynx had few games and even few hits to help selling a lot of Lynx.
By the time Psygnosis or Electronic Arts released for the Lynx, it was already too late: the Lynx were over flood by the GB in sales.
Marketing and advertisement were far in the advantage of the Nintendo because of the lack of resources of Atari.
I would summarize the Lynx failure by the fact that the Tramiel receipt: don't spend in ad, it will sold by itself was totally old fashioned in 1990.